Frequency And Class Bounderies-Statistics-Solved Assignments | Exercises Statistics

http://www.vustudents.net

Question:

defineclass frequency and class bounderies .

Answer: Class frequency: The no of observations falling in a particular class is called class frequency or simply frequency. Or The n

umbers in each class are referred to

as frequencies. Class Boundaries: Class boundaries are the precise numbers wh

ich separates one class from another. A class boundary located midway between

the upper limit of the class and the lower limit of the next higher class.

Question:

Define frequency curves and decomulatative frequency .

Answer: Frequency curves reveal the general pattern or shape of the distribution. When the frequencies are cumulated from the highest value to the lowest valu

e, it is

called a "more than" type cumulative frequency or decumulative frequency. It is used the to answer the questions like How

many students have weights more

than 100 pounds?

Question:

Define types of Frquency Curves?

Answer: Types of Frequency Curves: The frequency distribution occurring in practice, usually belong to one of the following four types. You will study about th

em in

your next lecture. 1.The Symmetrical Distribution. 2.Moderately Skewed Distribution. 3.Extremely Skewed or J-shaped Distribution 4.U-Shaped Distribution

Question:

HOw frequency distribution is formed from raw data?

Answer:

The frequency distribution of an ungrouped data is formed in the following steps. Step -

1 Identify the smallest and the largest measurements in the data set.

Step - 2 Find the range which is defined as the difference between the largest value and the smallest value. Step - 3 De

cide on the number of classes into which

the data are to be grouped. (By classes, we mean small sub-

intervals of the total interval) There are no hard and fast rules for this purpose. The decision will

depend on the size of the data. When the data are sufficiently large, the number of classes is usually taken between 10 and 20. Step -

4 Divide the range by the

chosen number of classes in order to obtain the approximate value of the class interval i.e. the width of our classes. Class interval is usually denoted by h. Step -

5 Decide the lower class limit of the lowest class. Where should we start from? The answer is that we should start constructi

ng our classes from a number equal

to or slightly less than the smallest value in the data. Step - 6 Determine the lower class limits of the successive classes by adding h successively. Step -

Determine the upper class limit of every class. The upper class limit of the highest class should cover the largest value in

the data. It should be noted that the

upper class limits will also have a difference of h between them. Step -

8 After forming the classes, distribute the data into the appropriate classes and find the

frequency of each class.

Question:

Give details to find the INTERVALS ?

Answer: Class interval: It is the length of class and is equal to the difference between the upper class boundary & lower class boundary. A uniform clas

s interval, usually

denoted by h or c.Determination of the class interval width The class interval width is determined by the using

following formula. Class interval h =

RANGE/No. of classes For Example: If the range of data is 61& its no. of classes is 10. Then its class interval = 61/10 = 6.1i.e. 6

Question:

Explain the hypergeometric experiment.

Answer: There are many experiments in which the condition of independence is violated and the probability of success does not remain constant for all trials

. Such

experiments are called Hypergeometric experiments. In other words, a Hypergeometric experiment has the following properties:

PROPERTIES OF

HYPERGEOMETRIC EXPERIMENT: i) The outcomes of each trial may be classified into one of two categories, success and failure. i

i) The probability of

success changes on each trial. iii) The successive trials are not independent. iv) The experim

ent is repeated a fixed number of times. The number of success, X

in a Hypergeometric experiment is called a Hypergeometric random variable and its probability distribution is called the Hype

rgeometric distribution. Consider

the example of a bag which contains 4 red balls and 6 black balls. If we draw 4 balls from the bag one by one without replacing the drawn balls into the bag

Let X be the number of red balls contained in the sample, then, it is a hypergeometric experiment because, (i) The result of each

draw may be classified as

either red (success) or black (failure). (ii) The probability of success changes on each draw. (iii) Successive draws are dep

endent as the selection is made

docsity.com

Partial preview of the text

Download Frequency And Class Bounderies-Statistics-Solved Assignments and more Exercises Statistics in PDF only on Docsity!

defineclass frequency and class bounderies. Class frequency: The no of observations falling in a particular class is called class frequency or simply frequency. Or The n umbers in each class are referred to as frequencies. Class Boundaries: Class boundaries are the precise numbers wh ich separates one class from another. A class boundary located midway between the upper limit of the class and the lower limit of the next higher class. Define frequency curves and decomulatative frequency. Frequency curves reveal the general pattern or shape of the distribution. When the frequencies are cumulated from the highest value to the lowest valu e, it is called a "more than" type cumulative frequency or decumulative frequency. It is used the to answer the questions like How many students have weights more than 100 pounds? Define types of Frquency Curves? Types of Frequency Curves: The frequency distribution occurring in practice, usually belong to one of the following four types. You will study about th em in your next lecture. 1.The Symmetrical Distribution. 2.Moderately Skewed Distribution. 3.Extremely Skewed or J-shaped Distribution 4.U-Shaped Distribution HOw frequency distribution is formed from raw data? The frequency distribution of an ungrouped data is formed in the following steps. Step - 1 Identify the smallest and the largest measurements in the data set. Step - 2 Find the range which is defined as the difference between the largest value and the smallest value. Step - 3 De cide on the number of classes into which the data are to be grouped. (By classes, we mean small sub- intervals of the total interval) There are no hard and fast rules for this purpose. The decision will depend on the size of the data. When the data are sufficiently large, the number of classes is usually taken between 10 and 20. Step - 4 Divide the range by the chosen number of classes in order to obtain the approximate value of the class interval i.e. the width of our classes. Class interval is usually denoted by h. Step - 5 Decide the lower class limit of the lowest class. Where should we start from? The answer is that we should start constructi ng our classes from a number equal to or slightly less than the smallest value in the data. Step - 6 Determine the lower class limits of the successive classes by adding h successively. Step -

Determine the upper class limit of every class. The upper class limit of the highest class should cover the largest value in the data. It should be noted that the upper class limits will also have a difference of h between them. Step - 8 After forming the classes, distribute the data into the appropriate classes and find the frequency of each class. Give details to find the INTERVALS? Class interval: It is the length of class and is equal to the difference between the upper class boundary & lower class boundary. A uniform clas s interval, usually denoted by h or c.Determination of the class interval width The class interval width is determined by the using following formula. Class interval h = RANGE/No. of classes For Example: If the range of data is 61& its no. of classes is 10. Then its class interval = 61/10 = 6.1i.e. 6 Explain the hypergeometric experiment. There are many experiments in which the condition of independence is violated and the probability of success does not remain constant for all trials

. Such experiments are called Hypergeometric experiments. In other words, a Hypergeometric experiment has the following properties:

PROPERTIES OF

HYPERGEOMETRIC EXPERIMENT: i) The outcomes of each trial may be classified into one of two categories, success and failure. i i) The probability of success changes on each trial. iii) The successive trials are not independent. iv) The experim ent is repeated a fixed number of times. The number of success, X in a Hypergeometric experiment is called a Hypergeometric random variable and its probability distribution is called the Hype rgeometric distribution. Consider the example of a bag which contains 4 red balls and 6 black balls. If we draw 4 balls from the bag one by one without replacing the drawn balls into the bag

Let X be the number of red balls contained in the sample, then, it is a hypergeometric experiment because, (i) The result of each draw may be classified as either red (success) or black (failure). (ii) The probability of success changes on each draw. (iii) Successive draws are dep endent as the selection is made

without replacement. (iv) The drawing is repeated a fixed number of times (n = 4) What are the concepts of sampling with replacement and sampling without replacement. In sampling with replacement, the units are replaced back before the next unit is selected. In this sampling procedure, number of units in population remains same for all selections. Let ‘N’ be the population size and ‘n’ be the sample size then number of possible samples that can b e drawn with replacement are Nn. In sampling without replacement, the units are not replaced back before the ne xt unit is selected. In this sampling procedure, number of units in population is reduced after each unit. Let ‘N’ be the population size and ‘n’ be the sample size then number of possible samples that can b e drawn with replacement are NCn . How we calculate the boundries? CLASS BOUNDARIES The true class limits of a class are known as its class boundaries.It should be noted that the difference be tween the upper class boundary and the lower class boundary of any class is equal to the class interval. What is Raw data ?And What is central tendency of variable data? Raw data: In statistics, a listing of values that has not yet been treated, arranged, or interpreted Measures of Center Tendency: In this context, the fir st thing to note is that in any data-based study, our data is always going to be variable. Plotting data in a frequency distribution shows the general shape of th e distribution and gives a general sense of how the numbers are bunched. Several statistics ca n be used to represent the "center" of the distribution. These statistics are commonly referred to as measures of central tendency. Such as Mean, Median & Mode. They remain unchanged by rearrangement of the observations in a different order. What is role of statics in the real life? Role of Statistics: Statistics is perhaps a subject that is used by everybody. In all areas, statistical techniques are being increasingly used, and are developing very rapidly. Statistics play its role in the real life which can be identified as follows.A businessman, an industrial and a research worker all employ tatistical methods in their work. Banks, Insurance companies and Government all have their statistics departments. A modern administrator whethe r in public or private sector leans on statistical data to provide a factual basis for decision. A politician uses statistics advantageously to lend support and credence to his arguments while elucidating the problems he handles. A social scientist uses statistical methods in various areas of socio- economic life 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”. Who was the founder of statics and probality? The word statistics ultimately derives from the New Latin term statisticum collegium ("council of state") and the Italian wor d statista ("statesman" or "politician"). The German Statistik, firs t introduced by Gottfried Achenwall (1749), originally designated the analysis of data about the state, signifying the "science of state" (then called political arithmetic in English). It acquired the meaning of the collection and classification of data ge nerally in the early 19th century. It was introduced into English by Sir John Sinclair. The mathematical methods of statistics emerged from probability theory, which can be dated to the correspondence of Pierre de Fermat and Blaise Pascal (1654). Christiaa n Huygens (1657) gave the earliest known scientific treatment of the subject. Jakob Bernoulli's Ars Conjectandi (posthumous, 1713) and Abraham de Moivre's Doctrine of Chances (1718) treated the subject as a br anch of mathematics.[1] In the modern era, the work of Kolmogorov has been instrumental in formulating the fundamental model of Probability Theory, which is used throughout statistics. What is the defination of Mid Range? MID-RANGE: If there are n observations with X0 and Xm as their smallest and largest observations respectively, then their mid- range is defined as Mid range= X0+ Xm / 2 It is obvious that if we add the smallest value with the largest, and divide by 2, we will get a value whic h is more or less in the middle of

Median is (n+1)/2 th value. b. If the no. of values is even then Median is the average of n/2 th and [(n/2) +1] th observations. Question: what is meant by imperical relation? Answer: Empirical Relationship: This is a concept which is not based on a mathematical formula; rather, it is based on observation. I n fact, the word ‘empirical’ implies ‘based on observation’. This is a rule of thumb that applies to data sets with frequency distributions that are mound- shaped and symmetric. According to this empirical rule: a) Approximately 68% of the measurements will fall within 1 standard deviation of the mean, i.e. within the interval (X – S,X + S) b) Approximately 95% of the measurements will fall within 2 standard deviations of the mean, i.e. within the interval (X – 2S,X + 2S). c) Approximately 100% (practically all) of the measurements will fall within 3 standard deviations of the mean, i.e. within the interval (X – 3S,X + 3S). Question: What is the relation between these two Moments & Moment Ratios? Answer: Moments: A moment designates the power to which deviations are raised before averaging them. Moment ratio: These are certain ratios in which both numerators and the denominators are moments. Question: what is difference between arbitrary form and dispersion? Answer: Arbitrary form: We find the moment form any value other than the mean that is called the moments about the arbitrary f orm. Dispersion: By which we mean the extent the observation in a sample or population are spread out. And the second moment about the mean is exactly the same thing as the variance, the positive square root of which is the standard deviation, the most important measure of dispersion? Question: what is the conditinal and un conditinal probability? Answer: In many situations, once more information becomes available, we are able to revise our estimates for the probability of further outcomes or events ha ppening. For example, suppose you go out for lunch at the same place and time every Friday and you are served lunch within 15 minutes with probability 0.9. However, given that you notice that the restaurant is exceptionally busy, the probability of being s erved lunch within 15 minutes may reduce to 0.7. This is the conditional probability of being served lunch within 15 minutes given that the restaurant is exceptionally busy Question: explain What is Moment ratios? Answer: Moment ratios are certain ratios in which both the numerator and the denominator are moments. The most common of these moment- ratios are denoted by b and b2 and defined by the relations: i) b1 = (m3)2 / (m2)3 ii) b2 = m4 / (m2)2 These are independent of origin and units of measuremen t, i.e. they are pure numbers. b1 is used to measure the Skewness of distribution, and b2 is used to measure the kurtosis of the distribution. Question: Why the significance level is consider 0.05? Answer: By a = 5%, we mean that there are about 5 chan ces in 100 of incorrectly rejecting a true null hypothesis. That is, we want to make the significance level as small as possible in order to protect the null hypothesis and to prevent, as far as possible, the investigator from inadvertently making false claims. Question: what is scatter diagram. what is its work ,and what is its advantages? Answer: A scatter plot is a useful summary of a set of bivariate data (two variables), usually drawn before working out a linear correlation coefficient or fittin g a regression line. It gives a good visual picture of the relationship between the two variables, and aids the interpretation of the correlation coefficient or regression model. Each unit contributes one point to the scatter plot, on which points are plot ted but not joined. The resulting pattern indicates the type and strength of the relationship between the two variables

Frequency And Class Bounderies-Statistics-Solved Assignments, Exercises of Statistics

Related documents

Partial preview of the text

Download Frequency And Class Bounderies-Statistics-Solved Assignments and more Exercises Statistics in PDF only on Docsity!

PROPERTIES OF