# Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 4 - Bivariate Frequency Distribution and Chi Square Statistic [Latest edition]

## Chapter 4: Bivariate Frequency Distribution and Chi Square Statistic

Exercise 4.1Exercise 4.2Miscellaneous Exercise 4
Exercise 4.1 [Page 49]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 4 Bivariate Frequency Distribution and Chi Square Statistic Exercise 4.1 [Page 49]

Exercise 4.1 | Q 1. (i) | Page 49

Following tale gives income (X) and expenditure (Y) of 25 families:

 Y/X 200 – 300 300 – 400 400 – 500 200 – 300 IIII I IIII I I 300 – 400 – IIII IIII I 400 – 500 – – II

Find Marginal frequency distributions of income and expenditure.

Exercise 4.1 | Q 1. (ii) | Page 49

Following tale gives income (X) and expenditure (Y) of 25 families:

 Y/X 200 – 300 300 – 400 400 –  500 200 – 300 IIII I IIII I I 300 – 400 – IIII IIII I 400 –  500 – – II

Find Conditional frequency distribution of X when Y is between 300 – 400.

Exercise 4.1 | Q 1. (iii) | Page 49

Following tale gives income (X) and expenditure (Y) of 25 families:

 Y/X 200 – 300 300 – 400 400 – 500 200 – 300 IIII I IIII I I 300 – 400 – IIII IIII I 400 – 500 – – II

Find Conditional frequency distribution of Y when X is between 200 – 300.

Exercise 4.1 | Q 1. (iv) | Page 49

Following tale gives income (X) and expenditure (Y) of 25 families:

 Y/X 200 – 300 300 – 400 400 – 500 200 – 300 IIII I IIII I I 300 – 400 – IIII IIII I 400 – 500 – – II

Find How many families have their income Rs. 300 and more and expenses Rs. 400 and less?

Exercise 4.1 | Q 2 | Page 49

Two dice are thrown simultaneously 25 times. The following price of observation are obtained.
(2, 3) (2, 5) (5, 5) (4, 5) (6, 4) (3, 2) (5, 2) (4, 1) (2, 5) (6, 1) (3, 1) (3, 3) (4, 3) (4, 5) (2, 5) (3, 4) (2, 5) (3, 4) (2, 5) (4, 3) (5, 2) (4, 5) (4, 3) (2, 3) (4, 1)
Prepare a bivariate frequency distribution table for the above data. Also, obtain the marginal distributions.

Exercise 4.1 | Q 3 | Page 49

Following data gives the age of husbands (X) and age of wives (Y) in years. Construct a bivariate frequency distribution table and find the marginal distributions.

 X 27 25 28 26 29 27 28 26 25 25 27 Y 21 20 20 21 23 22 20 20 19 19 23 X 26 29 25 27 26 25 28 25 27 26 Y 19 23 23 22 21 20 22 23 22 21

Find conditional frequency distribution of age of husbands when the age of Wife is 23 years.

Exercise 4.1 | Q 4 | Page 49

Construct a bivariate frequency distribution table of the marks obtained by students in English (X) and Statistics (Y).

 Marks inStatistics(X) 37 20 46 28 35 26 41 48 32 23 20 39 47 33 27 26 Marks inEnglish(Y) 30 32 41 33 29 43 30 21 44 38 47 24 32 21 20 21

Construct a bivariate frequency distribution table for the above data by taking class intervals 20 – 30, 30 – 40, ...... etc. for both X and Y. Also find the marginal distributions and conditional frequency distribution of Y when X lies between 30 – 40.

Exercise 4.1 | Q 5. (i) | Page 49

Following data gives height in cm (X) and weight in kgs (Y) of 20 boys. Prepare a bivariate frequency table taking class intervals 150-154, 155-159 ...etc. for X and 35-39, 40-44 ...etc. for Y. Also find Marginal frequency distributions.

Exercise 4.1 | Q 5. (ii) | Page 49

Following data gives height in cm (X) and weight in kgs (Y) of 20 boys. Prepare a bivariate frequency table taking class intervals 150-154, 155-159...etc. for X and 35-39, 40-44 ...etc. for Y. Also find conditional frequency distribution of Y when 155 ≤ X ≤ 159
(152, 40) (160, 54) (163, 52) (150, 35) (154, 36) (160, 49) (166, 54) (157, 38) (159, 43) (153, 48) (152, 41) (158, 51) (155, 44) (156, 47) (156, 43) (166, 53) (160, 50) (151, 39) (153, 50) (158, 46)

Exercise 4.2 [Pages 52 - 53]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 4 Bivariate Frequency Distribution and Chi Square Statistic Exercise 4.2 [Pages 52 - 53]

Exercise 4.2 | Q 1 | Page 52

Following table shows the classification of applications for secretarial and for sales positions according to gender. Calculate the value of χ2 Statistic.

 Offered Denied Male 75 150 Female 25 50
Exercise 4.2 | Q 2 | Page 53

200 teenagers were asked which take-out food do they prefer - French fries, burger, or pizza. The results were -

 French fries Burger Pizza Boys 6 20 24 Girls 18 40 92

Compute χ2 Statistics.

Exercise 4.2 | Q 3 | Page 53

A sample of men and women who had passed their driving test either in 1st attempt or in 2nd attempt surveyed. Compute χ2 statistics.

 Passed in → First attempt Second attempt Men 32 28 Women 8 12
Exercise 4.2 | Q 4 | Page 53

800 people were asked whether they wear glasses for reading with the following results.

 Age Wear glasses Do not wear glasses ≤ 30 310 90 > 30 290 110

Compute the χ2 square statistic.

Exercise 4.2 | Q 5. (a) | Page 53

Out of a sample of 120 persons in a village, 80 were administered a new drug for preventing influenza and out of them 18 were attacked by influenza. Out of those who were not administered the new drug, 10 persons were not attacked by influenza: Prepare a two-way table showing frequencies.

Exercise 4.2 | Q 5. (b) | Page 53

Out of a sample of 120 persons in a village, 80 were administered a new drug for preventing influenza and out of them 18 were attacked by influenza. Out of those who were not administered the new drug, 10 persons were not attacked by influenza: Prepare to compute the χ2 square statistic.

Miscellaneous Exercise 4 [Pages 53 - 55]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 4 Bivariate Frequency Distribution and Chi Square Statistic Miscellaneous Exercise 4 [Pages 53 - 55]

Miscellaneous Exercise 4 | Q 1. (i) | Page 53

Following data gives the coded price (X) and demand (Y) of a commodity.

 Price 5 7 9 8 10 7 9 8 5 11 11 10 2 3 9 Demand 9 15 13 15 14 10 11 14 10 14 6 14 15 11 12 Price 2 4 3 14 6 10 7 15 8 6 5 6 11 14 15 Demand 6 11 8 11 10 15 9 15 13 9 14 10 7 5 6

Classify the data by taking classes 0 – 4, 5 – 9, etc. for X and 5 – 8, 9 – 12, etc. for Y. Also find marginal frequency distribution of X and Y.

Miscellaneous Exercise 4 | Q 1. (ii) | Page 53

Following data gives the coded price (X) and demand (Y) of a commodity.

 Price 5 7 9 8 10 7 9 8 5 11 11 10 2 3 9 Demand 9 15 13 15 14 10 11 14 10 14 6 14 15 11 12 Price 2 4 3 14 6 10 7 15 8 6 5 6 11 14 15 Demand 6 11 8 11 10 15 9 15 13 9 14 10 7 5 6

Classify the data by taking classes 0 – 4, 5 – 9, etc. for X and 5 – 8, 9 – 12, etc. for Y. Also find conditional frequency distribution of Y when X is less than 10

Miscellaneous Exercise 4 | Q 2. (i) | Page 53

Following data gives the age in years and marks obtained by 30 students in an intelligence test.

 Age 16 17 22 19 21 16 Marks 16 19 39 50 48 41 Age 21 20 20 23 22 19 Marks 59 44 42 62 37 67 Age 23 20 22 22 23 22 Marks 45 57 35 37 38 56 Age 17 18 16 21 19 20 Marks 54 61 47 67 49 56 Age 17 18 23 21 20 16 Marks 51 42 65 56 52 48

Prepare a bivariate frequency distribution by taking class intervals 16 – 18, 18 – 20, … etc. for age and 10 – 20, 20 – 30, ... etc. for marks. Find marginal frequency distributions.

Miscellaneous Exercise 4 | Q 2. (ii) | Page 53

Following data gives the age in years and marks obtained by 30 students in an intelligence test.

 Age 16 17 22 19 21 16 Marks 16 19 39 50 48 41 Age 21 20 20 23 22 19 Marks 59 44 42 62 37 67 Age 23 20 22 22 23 22 Marks 45 57 35 37 38 56 Age 17 18 16 21 19 20 Marks 54 61 47 67 49 56 Age 17 18 23 21 20 16 Marks 51 42 65 56 52 48

Prepare a bivariate frequency distribution by taking class intervals 16 – 18, 18 – 20, … etc. for age and 10 – 20, 20 – 30, … etc. for marks. Find conditional frequency distribution of marks obtained when the age of students is between 20 – 22.

Miscellaneous Exercise 4 | Q 3. (i) | Page 54

Following data gives Sales (in Lakh Rs.) and Advertisement Expenditure (in Thousand Rs.) of 20 firms.
(115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68)
Construct a bivariate frequency distribution table for the above data by taking classes 115 – 125, 125 –135, ....etc. for sales and 60 – 62, 62 – 64, ...etc. for advertisement expenditure.

Miscellaneous Exercise 4 | Q 3. (ii) | Page 54

Following data gives Sales (in Lakh Rs.) and Advertisement Expenditure (in Thousand Rs.) of 20 firms.
(115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68)
Find marginal frequency distributions

Miscellaneous Exercise 4 | Q 3. (iii) | Page 54

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) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68) Conditional frequency distribution of Sales when the advertisement expenditure is between 64 – 66 (Thousand ₹)

Miscellaneous Exercise 4 | Q 3. (iv) | Page 54

Following data gives Sales (in Lakh Rs.) and Advertisement Expenditure (in Thousand Rs.) of 20 firms.
(115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68)
Conditional frequency distribution of advertisement expenditure when the sales are between 125 – 135 (lakh Rs.)

Miscellaneous Exercise 4 | Q 4. (i) | Page 54

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 denotes the age in years and Y denotes blood pressure for a group of 24 persons.
(55, 151) (36, 140) (72, 160) (38, 124) (65, 148) (46, 130) (58, 152) (50, 149) (38, 115) (42, 145) (41, 163) (47, 161) (69, 159) (60, 161) (58, 131) (57, 136) (43, 141) (52, 164) (59, 161) (44, 128) (35, 118) (62, 142) (67, 157) (70, 162)
Also, find Marginal frequency distribution of X.

Miscellaneous Exercise 4 | Q 4. (ii) | Page 54

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 denotes the age in years and Y denotes blood pressure for a group of 24 persons.
(55, 151) (36, 140) (72, 160) (38, 124) (65, 148) (46, 130) (58, 152) (50, 149) (38, 115) (42, 145) (41, 163) (47, 161) (69, 159) (60, 161) (58, 131) (57, 136) (43, 141) (52, 164) (59, 161) (44, 128) (35, 118) (62, 142) (67, 157) (70, 162)
Also, find Conditional frequency distribution of Y when X ≤ 45.

Miscellaneous Exercise 4 | Q 5 | Page 54

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.

 X 110 88 91 115 97 85 85 91 120 95 Y 500 800 870 599 625 650 905 700 850 824 X 82 105 99 90 108 124 90 90 111 89 Y 970 609 990 735 600 735 729 840 999 780 X 112 100 87 92 91 82 96 120 121 122 Y 638 850 630 720 695 923 555 810 805 526
Miscellaneous Exercise 4 | Q 6 | Page 54

Following table shows how the samples of Mathematics and Economics scores of 25 students are distributed:

 Marks in Economics Marks in Mathematics 40 – 70 70 – 100 40 – 70 20 15 70 – 100 5 10

Find the value of χ2 statistic.

Miscellaneous Exercise 4 | Q 7 | Page 54

Compute χ2 statistic from the following data:

Miscellaneous Exercise 4 | Q 8 | Page 54

Attitude of 250 employees towards a proposed policy of the company is as observed in the following table. Calculate the χ2 statistic.

 Favor Indifferent Oppose Male 68 46 36 Female 27 49 24
Miscellaneous Exercise 4 | Q 9 | Page 55

In a certain sample of 1000 families, 450 families are consumers of tea. Out of 600 Hindu families, 286 families consume tea. Calculate the χ2 statistic.

Miscellaneous Exercise 4 | Q 10 | Page 55

A sample of boys and girls were asked to choose their favourite sport, with the following results. Find the value of the χ2 statistic.

 Football Cricket Hockey Basketball Boys 86 60 44 10 Girls 40 30 25 5

## Chapter 4: Bivariate Frequency Distribution and Chi Square Statistic

Exercise 4.1Exercise 4.2Miscellaneous Exercise 4

## Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 4 - Bivariate Frequency Distribution and Chi Square Statistic

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Concepts covered in Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 4 Bivariate Frequency Distribution and Chi Square Statistic are Bivariate Frequency Distribution, Classification and Tabulation of Bivariate Data, Marginal Frequency Distributions, Conditional Frequency Distributions, Categorical Variables, Contingency Table, Chi-Square Statistic ( χ2 ).

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