Chapters
Chapter 2: Measures of Dispersion
Chapter 3: Skewness
▶ Chapter 4: Bivariate Frequency Distribution and Chi Square Statistic
Chapter 5: Correlation
Chapter 6: Permutations and Combinations
Chapter 7: Probability
Chapter 8: Linear Inequations
Chapter 9: Commercial Mathematics
Solutions for Chapter 4: Bivariate Frequency Distribution and Chi Square Statistic
Below listed, you can find solutions for Chapter 4 of Maharashtra State Board Balbharati for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board.
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]
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.
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.
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.
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?
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.
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.
Construct a bivariate frequency distribution table of the marks obtained by students in English (X) and Statistics (Y).
Marks in Statistics (X) |
37 | 20 | 46 | 28 | 35 | 26 | 41 | 48 | 32 | 23 | 20 | 39 | 47 | 33 | 27 | 26 |
Marks in English (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.
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.
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)
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]
Following table shows the classification of applications for secretarial and for sales positions according to gender. Calculate the value of χ^{2 }Statistic.
Offered |
Denied | |
Male | 75 | 150 |
Female | 25 | 50 |
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 χ^{2} Statistics.
A sample of men and women who had passed their driving test either in 1^{st} attempt or in 2^{nd} attempt surveyed. Compute χ^{2} statistics.
Passed in → |
First attempt | Second attempt |
Men | 32 | 28 |
Women | 8 | 12 |
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 χ^{2} square statistic.
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.
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 χ^{2 }square statistic.
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]
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.
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
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.
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.
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.
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
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 ₹)
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.)
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.
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.
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 |
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 χ^{2} statistic.
Compute χ^{2} statistic from the following data:
Graduates | Post-Graduates | |
Male | 28 | 22 |
Female | 32 | 18 |
Attitude of 250 employees towards a proposed policy of the company is as observed in the following table. Calculate the χ^{2} statistic.
Favor | Indifferent | Oppose | |
Male | 68 | 46 | 36 |
Female | 27 | 49 | 24 |
In a certain sample of 1000 families, 450 families are consumers of tea. Out of 600 Hindu families, 286 families consume tea. Calculate the χ^{2} statistic.
A sample of boys and girls were asked to choose their favourite sport, with the following results. Find the value of the χ^{2} statistic.
Football | Cricket | Hockey | Basketball | |
Boys | 86 | 60 | 44 | 10 |
Girls | 40 | 30 | 25 | 5 |
Solutions for Chapter 4: Bivariate Frequency Distribution and Chi Square Statistic
Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 4 - Bivariate Frequency Distribution and Chi Square Statistic
Shaalaa.com has the Maharashtra State Board Mathematics Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. Balbharati solutions for Mathematics Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Maharashtra State Board 4 (Bivariate Frequency Distribution and Chi Square Statistic) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
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 ).
Using Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board solutions Bivariate Frequency Distribution and Chi Square Statistic exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in Balbharati Solutions are essential questions that can be asked in the final exam. Maximum Maharashtra State Board Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board students prefer Balbharati Textbook Solutions to score more in exams.
Get the free view of Chapter 4, Bivariate Frequency Distribution and Chi Square Statistic Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board additional questions for Mathematics Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Maharashtra State Board, and you can use Shaalaa.com to keep it handy for your exam preparation.