Question 1

Question 1: Following data gives the coded price (X) and demand (Y) of a commodity. Classify the data by taking classes 0 – 4, 5 – 9, etc. for X and 5 – 8, 9 – 12, etc. for Y. Also find (i) ma

Accepted Answer

Given, X = coded price Y = demand Bivariate frequency table can be prepared by taking class intervals 0 – 4, 5 – 9,… etc for X and 5 – 8, 9 – 12,… etc for Y. Bivariate frequency distribution is as follows. (i) Marginal frequency distribution of X: Marginal frequency distribution of Y: (ii) Condition

Question 2

Question 2: Following data gives the age in years and marks obtained by 30 students in an intelligence test. Prepare a bivariate frequency distribution by taking class intervals 16 – 18, 18 –

Accepted Answer

Let X = Age in years Y = Marks Bivariate frequency table can be prepared by taking class intervals 16 – 18, 18 – 20,…, etc for X and 10 – 20, 20 – 30,…, etc for Y. Bivariate frequency distribution is as follows: (i) Marginal frequency distribution of X: Marginal frequency distribution of Y: (ii) Con

Question 3

Question 3: Following data gives Sales (in Lakh ?) and Advertisement Expenditure (in Thousand ₹) of 20 firms. (115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (1

Accepted Answer

(i) Let X = Sales (in lakh ₹) Y = Advertisement Expenditure (in Thousand ₹) Bivariate frequency table can be prepared by taking class intervals 115 – 125, 125 – 135, …. etc for X and 60 – 62, 62 – 64, ….etc for Y. Bivariate frequency distribution is as follows: (ii) Marginal frequency distribution o

Question 4

Question 4: Prepare a bivariate frequency distribution for the following data, taking class intervals for X as 35 – 45, 45 – 55, …. etc and for Y as 115 – 130, 130 – 145, … etc where, X denote

Accepted Answer

Given X = Age in years Y = Blood pressure Bivariate frequency table can be prepared by taking class intervals 35 – 45, 45 – 55, …, etc for X and 115 – 130, 130 – 145, ….., etc for Y. Bivariate frequency distribution is as follows: (i) Marginal frequency distribution of X: (ii) Conditional frequency

Question 5

Question 5: Thirty pairs of values of two variables X and Y are given below. Form a bivariate frequency table. Also find marginal frequency distributions of X and Y.

Accepted Answer

Bivariate frequency table can be prepared by taking class intervals 80 – 90, 90 – 100, etc for X and 500 – 600, 600 – 700, …., etc for Y. Bivariate frequency distribution is as follows: Marginal frequency distribution of X: Marginal frequency distribution of Y

Question 6

Question 6: The following table shows how the samples of Mathematics and Economics scores of 25 students are distributed: Find the value of ϰ2 statistic.

Accepted Answer

Table of observed frequencies. Expected frequencies are given by Eij = E11 = = 17.5 E12 = = 17.5 E21 = = 7.5 E22 = = 7.5 Table of expected frequencies.

Question 7

Question 7: Compute ϰ2 statistic from the following data:

Accepted Answer

Table of observed frequencies. Expected frequencies are given by Eij = E11 = = 30 E12 = = 20 E21 = = 30 E22 = = 20 Table of expected frequencies.

Question 8

Question 8: The attitude of 250 employees towards a proposed policy of the company is as observed in the following table. Calculate ϰ2 statistic.

Accepted Answer

Table of observed frequencies Expected frequencies are given by Eij = E11 = = 57 E12 = = 57 E13 = = 36 E21 = = 38 E22 = = 38 E23 = = 24 Table of observed frequencies.

Question 9

Question 9: In a certain sample of 1000 families, 450 families are consumers of tea. Out of 600 Hindu families, 286 families consume tea. Calculate ϰ2 statistic.

Accepted Answer

The given data can be arranged in the following table. Table of observed frequencies. Expected frequencies are given by Eij = E11 = = 270 E12 = = 330 E21 = = 180 E22 = = 220 Table of expected frequencies.

Question 10

Question 10: A sample of boys and girls were asked to choose their favourite sport, with the following results. Find the value of ϰ2 statistic.

Accepted Answer

Table of observed frequencies. Expected frequencies are given by Eij = E11 = = 84 E12 = = 60 E13 = = 46 E14 = = 10 E21 = = 42 E22 = = 30 E23 = = 23 E24 = = 5 Table of expected frequencies.

Chapter 4 Bivariate Frequency Distribution and Chi Square Statistic Miscellaneous Exercise 4 Solutions