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Question: what is Relative Frequency Answer: About tally bars: In construction of frequency distribution, when the number of observations is large, tally bars help us to avoid counting the numbers in the data again and again. If we use frequency numbers directly, we have to read whole data many times for determining the frequency of every class. So, tally bars save our time and energy. The numbers in each class are referred to as frequencies. Example: Suppose the numbers of children in 20 families are as follows: 2, 3, 0, 4, 4, 1, 5, 4,
8 We arrange these values in frequency distribution. Number of children Tally frequency 0 || 2 1 | 1 2 ||| 3 3 || 2 4 |||| 4
8 || 2 Total 20 Note that we have used two tally marks for 0, as it is repea ted two times and one tally mark for 1 as it is repeated once and three tally marks for 2 as it is repeated three times and so on. The relative frequency of a class is the frequency of th e class divided by the total number of frequencies of the class and i s generally expresses as a percentage. Example: The weights of 100 persons were given as under: Relative frequency table Weight No. of persons (f) Relative frequency 60 – 62 5 5/90 = 0.056 63 –
8/90 = 0.089 66 – 68 42 42/90 = 0.467 69 – 71 27 27/90 = 0.3 72 – 74 8 8/90 = 0.08 Total 90 Question: Define MEAN DEVIATION. Answer: Mean Deviation: As quartile deviation measures the dispersion of the data- set around the median. But the problem is that the sum of the deviations of the values from the mean is zero(No matter what the amount of dispersion in a data- set is, this quantity will always be zero, and hence it cannot be used to measure the dispersion in the data- set.) By ignoring the sign of the deviations we will achieve a NON-ZERO sum, and averaging these absolute differences, again, we obtain a non- zero quantity which can be used as a measure of dispersion. This quantity is known as the MEAN DEVIATION. As the absolute deviations of the observations from their mean are being averaged, therefore the complete name of this measure is Mean Absolute Deviation but generally, it is simply called “Mean Deviation”. Question: what is positively and negatively skewed?also explain about the what is CUMULATIVE FREQUENCY DISTRIBUTION. Answer: A frequency dist ribution or curve is said to be skewed when it departs from symmetry. If the right tail is longer the distribution is positively skewed and if the left tail of the distribution is longer, the distribution is said to be negatively skewed. Cumul ative frequency distribution: A cumulative frequency distribution is a plot of the number of observations falling in or below an interval. The graph shown here is a cumulative frequency distribution of the scores on a statistics test. Question: How can we make the class boundries? Answer: To find the class boundary of first class, firstly we find the difference between the upper class limit of first class (group ) and lower class limit of second class; secondly we divide that difference by two. Then we subtract that resulting value in each lower class limit of each class and add in upper class limit of each class in such a way we can make the class boundaries. For example: For the data given below, we can make class boundaries easily. Data: Class Limits Class Boundaries 3.5-4.4 3.45-4.45 4.5-5.4 4.45-5.45 5.5-
5.45-6.45 Firstly, we find the difference between 4.4(upper class limit of first class) and 4.5(lower class limit of second class). 4.5-4.4=0.1 Secondly, we divide the difference by 2. 0.1/2=0.05 Finally we su btract this resulting value from 3.5 and we get 3.45. And
then we add this value in 4.4 and we get 4.45 and so on. Question: why we use dot plot and what is the main purpose of this even we have so many other ways to plot the data Answer:
DOT PLOT: A
dot plot is a way of summarizing data, often used in exploratory data analysis to illustrate the major features of the distribution of the data in a convenient form. For nominal or ordinal data, a dot plot is similar to a bar chart, with the ba rs replaced by a series of dots. Each dot represents a fixed number of individuals. For continuous data, the dot plot is similar to a his togram, with the rectangles replaced by dots. A dot plot can also help detect any unusual observations (outliers), or any gaps in t he data set. The horizontal axis of a dot plot contains a scale for the quantitative variable that we want to represent. The numerical value o f each measurement in the data set is located on the horizontal scale by a dot. When data values repeat, the dots are placed above one another, forming a pile at that particular numerical location. Question: what is difference between Quartiles and percentiles. Answer: Quartile: The values which divide the distribution into four equal parts are called quartiles. Quartiles divide the data into four equal-sized and non- overlapping parts. One fourth of the data lies below the Q1 (first quartile). Half of the data lies below Q2 (second quartile) similarly, three quarters of the data lies below Q3 (third quartile) Note : Q2 (second quartile) is also known as median. Percentiles: Percentiles are values that divide a sample of data into one hundred groups containing (as far as possible) equa l numbers of observations. Question: What is the relation b/w Arthimetic, Geometric and Harmonic Mean explain mid-range as well. Answer: Relation between arithmetic mean, geometric mean and harmonic mean is given below: Arithmetic Mean > Geometric Mean >Harmonic Mean I.e. for a data arithmetic mean is greater than geometric mean and harmonic mean. And geometric mean is greater than harmonic mean. Mid Range: Mid range is the arithmetic mean of the smallest and largest value. Question: what is empirical relation and why we use it. Answer: Empirical Relation: In a single-peaked fre quency distribution, the values of mean, median & mode coincide if the frequency distribution is absolutely symmetrical. But if these values differ, the frequency distribution is said to be skewed. Experien ce has shown that in unimodel curve of moderate sk ew ness, the median is usually between mean& mode and between them the following approximate relation holds good. MEAN-MODE = 3(MEAN – MEDIAN) OR MODE = 3MEDIAN – 2MEAN The empirical relation does not hold in case of J-shaped or extremely skewed distribution. Question: How we select the number of classes for a given data set? Answer: The number of classes actually depends on the size of data. When the data are sufficiently large, the number of classes shoul d lie between 10 and 25. In the ranges provided by you the no of classes can be 5 , 10 or more because it depends upon the no of values in the data.As there is no hard & fast rule to determine the no of classes. H.A.Sturges has proposed an empirical rule for deter mining
respective classes. FREQUENCY POLYGON: A frequency polygon is obtained by plotting the class frequencies against the mid-points of the classes, and connecting the points so obtained by straight line segments Question: What is the importance of class boundaries? Answer: Class Boundaries: The true class limits of a class are known as its class boundaries It should be noted that the difference b etween the upper class boundary and the lower class boundary of any class is eq ual to the class interval. The problem with class intervals is the space between the intervals. To solve this problem, class boundaries are used. Class boundaries remove space between interval s by dividing it in half. One half is added to the upper limit o f one interval and the other half is subtracted from the lower limit of the next interval. By subtracting the class interval from upper class boundary of first class we can find the lower class boundary of first class. Question: Waht is the difference between Component bar chat and Multiple bar chart. Answer: We use the Component bar chart & Multiple bar chart according to the requirement of presentation of data. multiple bar & component bar chart to represent the two or more variables of the data. The component bar chart should be used when we have available to us information regarding totals and their components. But multiple bar charts should be used when we have the da ta, which do not add up to give us the totality of some one thing. e.g. imports & exports. Component bar charts: They are used to represent the cumulation of the various components of data & percentage. Multiple bar charts: Question: what is the telly and its adventages? Answer: TALLY MARKS: These are used to show that how many tim es a value appears in a data. This is a method of showing frequency of particular class. We use Tally marks for the convenience for making the frequency distribution as it used to record each & ev ery value fall in the particular class & after adding them we write it in the digit in the frequency column. Question: Explain the difference between interval and ratio scale and the concept of zero point in these scales. Answer: Interval Scale: A measurement scale possessing a constant interval size (distance ) but not a true zero point, is called an interval scale. Temperature measured on either the Celsius or the Fahrenheit scale is an outstanding example of interval scale because the sa me difference exists between 20o C (68o F) and 30o C (86o F) as between 5 o C (41o F) and 15o C (59o F). It cannot be said that a temperature of 40 degrees is twice as hot as a temperature of 20 degree, i.e. the ratio 40/20 has no meaning. The arithmetic operation of addition, subtraction, etc. is meaningful. Intervals between a djacent scale values are equal with respect the attribute being measured. E.g., the difference between 8 and 9 is the same as the difference between 76 and 77. Ratio Scale: It is a special kind of an interval scale where the sale of measurement has a true zero point as its origin. The ratio scale is used to measure weight, volume, distance, money, etc. There is a rationale zero point for the scale. Ratios are equivalent, e.g., the ratio of 2 to 1 is the same as the ratio of 8 to 4. The, key to differentiating interval and ratio scale is that the zero point is meaningful for ratio scale. Question: What is the differnce between statistics and statistic?
Answer: Statistics: Statistics is a branch of mathematics (i.e. Statistics is a subject) which involves the collection, organization, interpretation, and presentation of data (information). The goal is to make some sort of inference about the data that you have collected (i. e., more than half of the class spent one hour in doing a math homework) Statistic: It is a numerical quantity computed from the sample Question: Define absolute error. Answer: The difference between the measured value of a quantity and its actual value , given by This difference is called an absolute error. We use it because a contin uous variable can never be measured with perfect fineness because of certain habits and practices, methods of measurements, instruments used, etc. the measurements are thus always recorded correct to the nearest units and he nce are of limited accuracy. The actual or true values are, however, assumed to exist. For example, if a student’s weight is recorded as 60 kg (correct to the nearest kilogram), his true weight in fact lies between 59.5 kg and 60.5 kg, whereas a weight recorded as 60.00 kg means the true weight is known to lie between 59.995 and 60.005 kg. Thus there is a difference, however small it may be between the measured value and the true value. This sort of departure from the true value is technically known as the error of measur ement. In other words, if the observed value and the true value of a variable are denoted by x and x + e respectively, then the difference (x
e) – x, i.e. e is the error. This error involves the unit of measurement of x and is therefore called an absolute error. Question: What is cumulative frequency distributation? Answer: It is the tabular presentation of the number of data items whose numerical values is less than a given value. To obtain cumul ative frequency distribution, we add the frequencies of our frequency table column- wise, we obtain the column of cumulative frequencies. The Cumulative frequency of the last class is the sum of all frequencies in the distribution. Question: what is Strata and Stratum? Answer: A sample selected from a population which has been divided into a number of non- overlapping groups or sub populations called strata, such that part of the sample is drawn at random from each stratum. Question: Are quantitative and qualitative variables were same like Discrete and continuous variables? Answer: Quantitative Variable: It is a variable that can be measured numerically. e.g. heights, yield, age, weight. Data collected on such a variable are called quantitative data It is of two types: (i) Discrete Random Variable A discrete random var iable is one that can take only a discrete set of integers or whole numbers. For discrete variables values are obtained by counting process. For example , if we toss three dice together, and let X denote the number of heads, then the random variable X consi sts of the values 0, 1, 2, and 3. Obviously, in this example, X is a discrete random variable A discrete random variable represents count data such as the numb er of persons in a family, the number of rooms in a house, the number of deaths in an accident, t he income of an individual, etc. (ii) Continuous Random Variable A variable is called a continuous variable if it can take on any value-fractional or integral–– within a given interval, i.e. its domain is an interval with all possible values without gaps. F or continuous variables values are obtained by measuring process. A continuous variable represents measurement data such as the age of a person, the height of a plant, the weight
state, for example, information about the sizes of population sand armed forces. But this word has now acquired different meanings.
- In the first place, the word statistics refers to “numerical facts systematically arranged”. In this sense, the word statis tics is always used in plural. We have, for instance, statistics of prices, statistics of road accidents, stati stics of crimes, statistics of births, statistics of educational institutions, etc. In all these examples, the word statistics denotes a set of numerical data in the respectiv e fields. This is the meaning the man in the street gives to the word Statistics and most people usually use the word data instead. • In the second place, the word statistics is defined as a discipline that includes procedures and techniques used to collect process and ana lyze numerical data to make inferences and to research decisions in the face of uncertainty. It should of course be borne in mind that uncertainty does not imply ignorance but it refers to the incompleteness and the instability of data available. In this sense , the word statistics is used in the singular. As it embodie s more of less all stages of the general process of learning, sometimes called scientific method, statistics is characterized as a science. Thus the word statistics used in the plural refers to a set of numerical in formation and in the singular, denotes th e science of basing decision on numerical data. It should be noted that statistics as a subject is mathematical in character. • Thirdly, the word statistics are numerical quantities calculated from sample observations; a sin gle quantity that has been so co llected is called a statistic. The mean of a sample for instance is a statistic. The word statistics is plural when used in this sense. Formal Definition of Statistics: Statistics is a branch of mathematics which involves the collection
organization, inte rpretation, and presentation of data (information). The goal is to make some sort of inference about the data that you have collected (i.e., more than half of the class spent one hour in doing a math homework). Question: Define sample and Probability. Answer: Sample: A sample is a group of units selected from a larger group (the population). By studying the sample it is hoped to dra w valid conclusions about the larger group Probability: A probability provides a quantitative description of the likely occ urrence of a particular event. Probability is conventionally expressed on a scale from 0 to 1; a rare event has a probability close to 0, a very common event has a probability close to 1 Question: what is startified random sampling? Answer: Stratified Sampling: A stratified sample is obtained by taking samples from each stratum or sub- group of a population. When we sample a population with several strata, we generally require that the proportion of each stratum in the sample should be the same as in th e population. Stratified sampling techniques are generally used when the population is heterogeneous, or dissimilar, where certain homogeneous, or similar, sub- populations can be isolated (strata). Simple random sampling is most appropriate when the entire population from which the sample is taken is homogeneous. Some reasons for using stratified sampling over simple random sampling are: the cost per observation in the survey may be reduced; estimates of the population parameters may be wanted for each sub-population; Increased accuracy at given cost. Question: What is Simple Random Sampling? Answer: Simple Random Sampling: Simple random sampling is the basic sampling technique where we select a group of subjects (a sample) for study from a larger group (a population). Each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample. Every possible sample of a given size has the same chance of selection; i.e. ea ch
member of the population is equally likely to be chosen at any stage in the sampling process Question: what are the basic statistical techniques. Answer: summarization, graphical representation, averages, dispersion, regression, correlation, index number are basic statistical techniques. Question: Statistics can help in computer give an example. Answer: Statistics is a science of facts and figures. This subject is equally important as other subjects. Statistics is a discipline that has finds application in the most diver se fields of activity. It is perhaps a subject that should be used by everybody. Statistical techniques being powerful tools for analyzing numerical data are used in almost every branch of learning. In all areas, statistical techniques are being increasing ly used, and are developing very rapidly. Statistics is Information Science and Information Science is Statistics. It is an applicable science as its tools are applied to all sciences including humanities and social sciences. Question: Explain the measuring scales with examples. Answer: Measurement Scales: By measurement scale, we usually mean the assigning of number to observations or objects and scaling is a process of measuring. The four scales of measurements are briefly mentioned below: NOMINAL SCA LE: The classification or grouping of the observations into mutually exclusive qualitative categories or classes is said to constitute a nominal scale. Example: Students are classified as male and female. Number 1 and 2 may also be used to identify these t wo categories.. ORDINAL OR RANKING SCALE: It includes the characteristic of a nominal scale and in addition has the property of ordering or ranking of measurements. For example, the performance of students (or players) is rated as excellent, good fair or p oor, etc. Number 1, 2, 3, 4 etc. are also used to indicate ranks. The only relation that holds between any pair of categories is that of “greater than” ( or more preferred). INTERVAL SCALE: A measurement scale possessing a constant interval size (distance) but not a true zero point, is called an interval scale. Example: Temperature measured on either the Celsius or the Fahrenheit scale is an outstanding examp le of interval scale because the same difference exists between 20o C (68o F) and 30o C (86o F) as be tween 5o C (41o F) and 15o C (59o F). It cannot be said that a temperature of 40 degrees is twice as hot as a temperature of 20 degree, i.e. the ratio 40/20 ha s no meaning. The arithmetic operation of addition, subtraction, etc. is meaningful. RATIO SCALE: It is a special kind of an interval scale where the sale of measurement has a true zero point as its origin. The ratio scale is used to measure weight, volume, d istance, money, etc. The, key to differentiating interval and ratio scale is that the zero point is meaningful for ratio scale Question: Is internet the cheapest mode for statistical calculation? What kind of graphs do we need for this subject? What is the Trad itional method of writing down the statistical data/information? Are there any progr ams(Comuter Softwares) of Statistics for appropriate manipulation of the data? What kind of scale is most commonly used in our country? Answer: Is internet the cheapest mode for statistical calculation? Statistics is a discipline that has finds applicatio n in the most diverse fields of activity. It is perhaps a subject that should be used by everybody. Statistical techniques being powerful tools for analyz ing numerical data are used in almost every branch of learning. In all areas, statistical techniques a re being increasingly used, and are developing very rapidly. data sent over the Internet consists of discrete packets that can follow different channels in a seq uence over
powerful tools for analyzing numerical data are used in almost every branch of learning. In all areas, statistical techniques are being increasingly used, and are developing very rapidly. Statistics is In formation Science and Information Science is Statistics. It is an applicable science as its tools are applied to all sciences including humanities and social sciences. Statistics is divided i nto two main areas: Descriptive Statistics; all the charts, table s and graphs are examples of descriptive statistics. Probability theory is not needed for this part. Inferential Statistics; all the statistical tests in inferential statistics are based on probability theory. W e can safely say that probability theory is t he backbone of Inferential Statistics. The Importance of Statistics H.G. Wells anticipated that statistical thinking (numerical literacy) would one day be as necessary for efficient citizenship as the ability to read and write. Stati stics allows a trained person to see the significance of data, the relationship between seemingly unrelated phenomena, and predict what may happen in the future or determine what may have happened in the past. The study and collection of data are important in the w ork of many pr ofessions, so that training in the science of statistics is valuable preparation for a variety of careers. Each month, for example, Government statistical offices release the latest numerical information on unemployment and inflation. Economists an d financ ial advisors as well as policy makers in government and business study these data to make informed decisions. Market research data that reveal consumer tastes influence business decisions. Farmers study data from field trials of new crop vari eties. Engineers gather data on the quality and reliability of manufactured products. Insurance agencies use actuary tables to determine th e likelihood that you will have a car accident and will adjust your premiums accordingly. Doctors must understand the origin an d trustworthiness of the data that appear in medical journals if they are to offer their patients the most effective treatment Do ctors can determine the likelihood that you will develop cancer or a have a heart attack. Political scientists use statistics to de termine how citizens feel about current issues and their likelihood to vote for a particular candidate. Statistics is a science of facts and figures. This subject is equally important as other subjects. Statistics is a discipline that has finds application in the most diverse fields of activity. It is perhaps a subject that should be used by everybody. Statistical techniques being powerful tools for analyzing numerical data are used in almost every branch of learning. In all areas, statistical techniques ar e being increasingly used, and are developing very rapidly. Statistics is Information Science and Information Science is Statistics. It is an applicable science as its too ls are applied to all sciences including humanities and social sciences. Statistics i s divided into two main areas: Descriptive Statistics; all the charts, tables and graphs are examples of descriptive statistics. Probability theory is not needed for this part. Inferential Statistics; all the statistical tests in inferential statistics are based on probability theory. We can safely say that probability theory is the backbone of Inferential Statistics. The Importance of Statistics H.G. Wells anticipated that statistical thinking (numerical literacy) would one day be as necessary for efficien t citizenship as the ability to read and write. Statistics allows a trained person to see the significance of data, the relationship between seemingly unrelated phenomena, and predict what may happen in the future or determine what may have happened in the past. The study and collection of data are important in the work of many professions, so that training in the science of statistics is valuable preparation for a variety of careers. Each month, for example, Government statistical offic es release the lates t numerical information on unemployment and inflation. Economists and financial advisors as well as policy makers in government and business study these data to make informed decisions. Market research data that reveal consumer tastes influen ce business de cisions. Farmers study data from field trials of new crop varieties. Engineers gather data on the quality and reliability of manufactured products. Insurance agencies use actuary tables to determine the likelihood that you will have a car accident and will adjust your premiums accordingly. Doctors must understand the origin and trustworthiness of the data that appear in medical journals if they are to offer their patients the most effective treatment Doctors can determine the likelihood that you will develo p cancer or a have a heart attack. Political scientists use statistics to determine how citizens feel about current issues and their
likelihood to vote for a particular candidate. Question: What is the roal of Statistics and Probability in BS(Commerce). Answer: The Importance of Statistics H.G. Wells anticipated that statistical thinking (numerical literacy) would one day be as necess ary for efficient citizenship as the ability to read and write. · Statistics allows a trained person to see the significa nce of data, the relationship between seemingly unrelated phenomena, and predict what may happen in the future or determine what may have happened in the past. The study and collection of data are important in the work of many professions, so that training in the science of statistics is valuable preparation for a variety of careers. Each month, for example, Government statistical offices release the latest num erical information on unemployment and inflation. Economists and financial advisors as well as pol icy makers in government and business study these data to make informed decisions. Market research data that reveal consumer tastes influence business decisions. F armers study data from field trials of new crop varieties. · Insurance agencies use actuary t ables to determine the likelihood that you will have a car accident and will adjust your premiums accordingly. A modern administrator whether in public or private sector lea ns on statistical data to provide a factual basis for decision. A businessman, an i ndustrial and a research worker all employ statistical methods in their work. Banks, Insurance companies and Government all have their statistics departments. A social scientist us es statistical methods in various areas of socio-economic life of a nation. It is sometimes said that “a social scientist without an adequate understanding of statistics, is often like the blind man groping in a dark room for a black cat that is not there. Question: what is the difference between inferential and descriptive statistics? Answer: Descriptive Statistics: Methods of organizing, summarizing, and presenting of data in an informative way. Its grounds are mea sure of central tendency and measure of dispersion. Inferential statistics: The methods used to find out somethi ng about a population, based on a sample. Question: What is the role of Statistics and Probability concerned to Information Technology and what is meant Probability? Answer: The Importance of Statistics H.G. Wells anticipated that statistical thinking (numerical literacy) would one day be as necessary for efficient citizenship as the ability to read and write. Statistics allows a trained person to see the significance of data, t he relationship between seemingly unrelated phenomena, and predict what may happen in the future or determine what may have happened in the past. The study and collection of data are important in the work of many professions, so that training in the science of stat istics is valuable preparation for a variety of careers. Each mont h, for example, Government statistical offices release the latest numerical information on unemployment and inflation. Economists and financial advisors as well as policy makers in government and busin ess study these data to make informed decisions. Market research data that reveal consumer tastes influence business decisions. Farmers study data from field trials of new crop varieties. Engineers gather data on the quality and reliability of manufactured prod ucts. Insurance agencies use actuary tables to det ermine the likelihood that you will have a car accident and will adjust your premiums accordingly. Doctors must understand the origin and trustworthiness of the data that appear in medical journals if they are t o offer their patients the most effective tre atment Doctors can determine the likelihood that you will develop cancer or a have a heart attack. Political scientists use statistics to determine how citizens feel about current issues and their likelihood to vote for a pa rticular candidate. IMPORTANCE O F STATISTICS IN VARIOUS FIELDS As stated earlier, Statistics is a discipline that has finds
