Statistical Error-Statistics-Solved Assignments, Exercises of Statistics

Statistics study consist on topics like F distribution, multiplication theorems, probability, random variable, T distribution, geometric probability distribution, marginal probability, sampling, skewness, symmetrical distribution and transformation, estimates. This solved assignment includes: Statistical, Error, Ordinal, Scale, Finite, Population, Quota, Random, Sampling, Frequency, Frequency, Polygon, Bar, Pie, Chart

Typology: Exercises

2011/2012

Uploaded on 08/12/2012

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Question:
What is statistical error, in what way it differs from a mistake?
Answer: Statistical error: A continuous 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 hence are of limited accuracy. In sta
tistics the error does not
mean mistake which is a chance of in accuracy because the actual or true values are, however, assumed to exist.
Question:
What is the difference between a nominal and an ordinal scale?
Answer: ORDINAL SCALE It includes the characteristic of a nominal scale and in addition has the property of ordering or ranking of me
asurements. For example, the
performance of students (or players) is rated as excellent, good fair or poor, etc. Number 1, 2, 3, 4 etc. are also used to indicate ranks
Question:
What is Finite population and Infinite population?
Answer: Finite Population: The population is Finite when it
contains countable number of units. Examples: 1.Population of all licensed cars. 2.Population of all students
in college. 3.Population of all houses in a country. Infinite Population: The population is Infinite when it contains uncountable number of units.
Examples:
1.Population of all points in line. 2.Population of pressures at various points in the atmosphere.
Question:
Which is better QUOTA SAMPLING or RANDOM SAMPLING?
Answer: Both Random & Quota sampling has their advantages & disadvantages. Both
are used by organizations for their surveys. 1.The main advantage of Random
sampling is that it provides a valid estimate of sampling error, But it is impossible to assess objectively the error in quot
cheap (and fast) it is usually done poorly. When it is done better, it is not all much cheaper really then efficient probability (Random) sampl
ing. Random
sampling is widely used in various areas such as industry, agriculture, business etc.
Question:
Define grouped data, ungrouped data and frequency.
Answer: Grouped data - Data available in class intervals as summarized by a frequency distribution. Individual values of the original data are not a
vailable. Or Data that
are presented in the form of frequency distribution
are called grouped data. We often group the data of a sample into intervals to produce a better over all
picture of the unknown population, but in doing so we lose the identity of individual observations in the sample. Ungrouped data - Ungrouped data is th
at in
which raw data is not grouped. Example: 2, 3, 9, 0, 4, 4, 1, 5, 4, 8, 5, 3, 6, 6, 0, 2, 2, 7, 6, 4, 8, 4, 3, 3, 1, 0, 8, 7, 5
, 1, 3, 4, 7, 2, 4, 7, 5, 2, 6, 3, 1, 7, 5, 4, 6, 4, 2,
5, 3, 4, Definition of frequency: Number of observations in each clas
s or group is called is the frequency of that class. It means “how frequently something
happens?”
Question:
In which situation we use Pie chart simple, Bar chart and multiple bar chart ?
Answer: Pie Chart consists of a circle divided into sectors whos
e areas are proportional to the various parts into which the whole quantity is divided. It is an effective
way of showing percentage parts when the whole quantity is taken as 100. It is also used when the basic categories are not quantifiable. For example
as with
expenditure, classified into food, clothing, fuel and light etc. Simple Bar Diagram is used when the data consist of a single
component and do not involve much
variation. Multiple Bar Diagram is used represent two or more related sets of data. It is a diagram which supplies more than one information at the same time.
Question:
Brifly decribe the primary data and secondary data.
Answer: Primary Data: Primary data are data collected by the investigators for the purposes of the study. This allows t
he opportunity to improve precision and to
minimize measurement bias through the use of precise definitions, systematic procedures, trained observers, and blinding duri
ng data collection. Such data are
usually expensive to acquire compared to secondary dat
a. Secondary Data: Secondary data are data collected for purposes other than that of the study, such as
patient clinical records, and are used frequently for case-control studies. Because the investigator has no control over definitions, collection procedu
res,
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Question: What is statistical error, in what way it differs from a mistake? Answer: Statistical error: A continuous 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 hence are of limited accuracy. In sta tistics the error does not mean mistake which is a chance of in accuracy because the actual or true values are, however, assumed to exist. Question: What is the difference between a nominal and an ordinal scale? Answer: ORDINAL SCALE It includes the characteristic of a nominal scale and in addition has the property of ordering or ranking of me asurements. For example, the performance of students (or players) is rated as excellent, good fair or poor, etc. Number 1, 2, 3, 4 etc. are also used to indicate ranks Question: What is Finite population and Infinite population? Answer: Finite Population: The population is Finite when it contains countable number of units. Examples: 1.Population of all licensed cars. 2.Population of all students in college. 3.Population of all houses in a country. Infinite Population: The population is Infinite when it contains uncountable number of units. Examples: 1.Population of all points in line. 2.Population of pressures at various points in the atmosphere. Question: Which is better QUOTA SAMPLING or RANDOM SAMPLING? Answer: Both Random & Quota sampling has their advantages & disadvantages. Both are used by organizations for their surveys. 1.The main advantage of Random sampling is that it provides a valid estimate of sampling error, But it is impossible to assess objectively the error in quot a sampling. 2.When quota sampling is cheap (and fast) it is usually done poorly. When it is done better, it is not all much cheaper really then efficient probability (Random) sampl ing. Random sampling is widely used in various areas such as industry, agriculture, business etc. Question: Define grouped data, ungrouped data and frequency. Answer: Grouped data - Data available in class intervals as summarized by a frequency distribution. Individual values of the original data are not a vailable. Or Data that are presented in the form of frequency distribution are called grouped data. We often group the data of a sample into intervals to produce a better over all picture of the unknown population, but in doing so we lose the identity of individual observations in the sample. Ungrouped data - Ungrouped data is th at in which raw data is not grouped. Example: 2, 3, 9, 0, 4, 4, 1, 5, 4, 8, 5, 3, 6, 6, 0, 2, 2, 7, 6, 4, 8, 4, 3, 3, 1, 0, 8, 7, 5

5, 3, 4, Definition of frequency: Number of observations in each clas s or group is called is the frequency of that class. It means “how frequently something happens?” Question: In which situation we use Pie chart simple, Bar chart and multiple bar chart? Answer: Pie Chart consists of a circle divided into sectors whos e areas are proportional to the various parts into which the whole quantity is divided. It is an effective way of showing percentage parts when the whole quantity is taken as 100. It is also used when the basic categories are not quantifiable. For example as with expenditure, classified into food, clothing, fuel and light etc. Simple Bar Diagram is used when the data consist of a single component and do not involve much variation. Multiple Bar Diagram is used represent two or more related sets of data. It is a diagram which supplies more than one information at the same time. Question: Brifly decribe the primary data and secondary data. Answer: Primary Data: Primary data are data collected by the investigators for the purposes of the study. This allows t he opportunity to improve precision and to minimize measurement bias through the use of precise definitions, systematic procedures, trained observers, and blinding duri ng data collection. Such data are usually expensive to acquire compared to secondary dat a. Secondary Data: Secondary data are data collected for purposes other than that of the study, such as patient clinical records, and are used frequently for case-control studies. Because the investigator has no control over definitions, collection procedu res,

observers (clinicians) or other opportunities for measurement bias reduction, the opportunity for bias is large. The advantag es of secondary data are that these data are usually considerably less expensive and much more readily available than are prim ary data. The severe disadvantage is the opportunity for the presence of large amounts of measurement bias. Question: define Frequency Polygon. Answer: A frequency polygon is obtained by plotting the class frequencies against the mid-points of the cl asses, and connecting the points so obtained by straight line segments. In order to construct the frequency polygon, the mid-points of the classes are taken along the X-axis and the frequencies along the Y-axis. Question: Explian how you allocate frequency.And also explain bivarite table? Answer: Steps in Frequency Distribution: Following are the basic rules to construct frequency distribution: 1. Decide the number of c lasses into which the data are to be grouped & it depends upon the size of data. 2. Determine the RANGE (difference between the smallest &largest values in data) of data. 3. Decide where to locate the class limit (numbers typically use to identify the classes). 4. Determine the reaming class limits by adding the class interval repeatedly.

  1. Distribute the data into classes by using tally marks and sum it in frequency column. Finally, total the frequency column to see that al l data have been accounted for. Bivarite Table: In bivarite frequency table we have two variables & their respective frequencies. Question: Define interval in simple words. Answer: Class interval is defined as the length of class which is equal to the difference between the upper boundary and the lower bo undary of the class. Class interval is usually denoted by h. Or Class interval is obtained by finding the difference between either two successive upper class limits or lower class limit s. Note that the lower class limits should not be subtracted from its upper limit to get the class interval. Suppose we have the fo llowing frequency distribution: Class Limits Class boundaries f 5 – 9 4.5 – 9.5 2 10 – 14 9.5 – 14.5 5 15 – 19 14.5 – 19.5 9 20 – 24 19.5 – 24.5 12 25 – 29 24.5 – 29.5 3 Here class interval is 5 Question: What is the procedure of Tally? Answer: TALLY MARKS: These are used to show that how many times a value appears in a data. This is a method of showing frequency of particu lar class. Example: If the no 4appears one time in the data then in column of tally we use l.But if it appears four times then we use llll. Question: What are definitions of Bivariate & Univariate? Answer: BIVARITE TABLE: In bivarite frequency table we have two variables & their frequency. Example: Medium of schooling and sex of the students of a particular college. UNIVARITE TABL E: In unviarite frequency table we have one variable & its frequency. Example: Medium of schooling of the students of a particular college. Question: Is there any ASYMMETRICAL DISTRIBUTIONS and also What can we say about Raito Charts or Semi-Logarithmic Graphs? Answer: Asymmetrical Distribution: The Moderately Skewed Distribution is also known as Asymmetrical Distribution. Frequency distribut ion or curve is said to be “Skewed” when it departs from symmetry. In this the frequencies tend to pile up at on e end or the other end of the distribution or curve .This is the most common type. Ratio Charts or Semi- Logarithmic Graph: In ordinary types of graph, the scales used are called the natural scales or the arithmetic scales. These graphs can only be used to compare absolute changes. More often than not we are interested in studying relative changes or ratio. In practice , the diff iculty of looking up logarithms can be dispensed with using another type of graph paper ,called Semi-logarithmic paper or ratio pap er. “Graphs obtained by plotting the values on Semi-logarithmic paper or ratio paper and joining the successive points by means of straight line segments are called Semi- logarithmic Graph or Ratio Graph”.