# Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 1 - Partition Values [Latest edition]

## Chapter 1: Partition Values

Exercise 1.1Exercise 1.2Exercise 1.3Miscellaneous Exercise 1
Exercise 1.1 [Pages 7 - 8]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 1 Partition Values Exercise 1.1 [Pages 7 - 8]

Exercise 1.1 | Q 1 | Page 7

Compute all the quartiles for the following series of observations:
16, 14.9, 11.5, 11.8, 11.1, 14.5, 14, 12, 10.9, 10.7, 10.6, 10.5, 13.5, 13, 12.6.

Exercise 1.1 | Q 2 | Page 7

The heights (in cm) of 10 students are given below: 148, 171, 158, 151, 154, 159, 152, 163, 171, 145. Calculate Q1 and Q3 for above data.

Exercise 1.1 | Q 3 | Page 7

Monthly consumption of electricity (in units) of families in a certain locality is given below:

205, 201, 190, 188, 195, 172, 210, 225, 215, 232, 260, 230.

Calculate electricity consumption (in units) below which 25% of families lie.

Exercise 1.1 | Q 4 | Page 7

For the following data of daily expenditure of families (in ₹), compute the expenditure below which 75% of families include their expenditure.

 Daily expenditure (in ₹) 350 450 550 650 750 No. of families 16 19 24 28 13
Exercise 1.1 | Q 5 | Page 7

Calculate all the quartiles for the following frequency distribution:

 No. of E-transactions per day 0 1 2 3 4 5 6 7 No. of days 10 35 45 95 64 32 10 9
Exercise 1.1 | Q 6 | Page 7

The following is the frequency distribution of heights of 200 male adults in a factory:

 Height (in cm.) No. of male adults 145 – 150 4 150 – 155 6 155 – 160 25 160 – 165 57 165 – 170 64 170  – 175 30 175 – 180 8 180 – 185 6

Find the central height.

Exercise 1.1 | Q 7 | Page 7

The following is the data of pocket expenditure per week of 50 students in a class. It is known that the median of the distribution is ₹120. Find the missing frequencies.

 Expenditure per week(in ₹) 0 – 50 50 – 100 100 – 150 150 –200 200 –250 No. of students 7 ? 15 ? 3
Exercise 1.1 | Q 8 | Page 8

The following is the distribution of 160 Workers according to the wages in a certain factory:

 Wages more than(in ₹) No. of workers 8000 160 9000 155 10000 137 11000 91 12000 57 13000 23 14000 10 15000 1 16000 0

Determine the values of all quartiles and interpret the results.

Exercise 1.1 | Q 9 | Page 8

Following is the grouped data for duration of fixed deposits of 100 senior citizens from a certain bank:

 Fixed deposit (in days) 0 – 180 180 – 360 360 – 540 540 – 720 720 – 900 No. of senior citizens 15 20 25 30 10

Calculate the limits of fixed deposits of central 50% senior citizens.

Exercise 1.1 | Q 10 | Page 8

Find the missing frequency given that the median of the distribution is 1504.

 Life in hours 950 – 1150 1150 – 350 1350 – 1550 1550 – 1750 1750 – 1950 1950 – 2150 No. of bulbs 20 43 100 – 23 13
Exercise 1.2 [Pages 15 - 16]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 1 Partition Values Exercise 1.2 [Pages 15 - 16]

Exercise 1.2 | Q 1 | Page 15

Calculate D6 and P85 for the following data:
79, 82, 36, 38, 51, 72, 68, 70, 64, 63.

Exercise 1.2 | Q 2 | Page 15

The daily wages (in Rs.) of 15 laboures are as follows:
230, 400, 350, 200, 250, 380, 210, 225, 375, 180, 375, 450, 300, 350, 250
Calculate D8 and P90.

Exercise 1.2 | Q 3 | Page 15

Calculate 2nd decide and 65th percentile for the following:

 x 80 100 120 145 200 280 310 380 400 410 f 15 18 25 27 40 25 19 16 8 7
Exercise 1.2 | Q 4 | Page 15

From the following data calculate the rent of 15th, 65th and 92nd house.

 House rent (in ₹) 11000 12000 13000 15000 14000 16000 17000 18000 No. of houses 25 17 13 14 15 8 6 2
Exercise 1.2 | Q 5 | Page 15

The following frequency distribution shows the weight of students in a class:

 Weight (in Kg) 40 45 50 55 60 65 Number of Students 15 40 29 21 10 5

(a) Find the percentage of students whose weight is more than 50 kg.
(b) If the weight column provided is of mid values then find the percentage of students whose weight is more than 50 kg.

Exercise 1.2 | Q 6 | Page 15

Calculate D4 and P48 from the following data:

 Mid value 2.5 7.5 12.5 17.5 22.55 Total Frequency 7 18 25 30 20 100
Exercise 1.2 | Q 7 | Page 15

Calculate D6 and P20 of the following distribution

 Length (in inches) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120 No. of units 1 14 35 85 90 15
Exercise 1.2 | Q 8 | Page 16

Weekly Wages for group of 100 persons are given below:

 Wages(in ₹) 0 – 500 500 – 1000 1000 – 1500 1500 – 2000 2000 – 2500 No. of persons 7 ? 25 30 ?

D3 for this group is ₹1100 Calculate the missing frequencies.

Exercise 1.2 | Q 9 | Page 16

The weekly profit (in rupees) of 100 shops are distributed as follows:

 Profit per shop No. of shops 0 – 1000 10 1000 – 2000 16 2000 – 3000 26 3000 – 4000 20 4000 – 5000 20 5000 – 6000 5 6000 – 7000 3

Find the limits of the profit of middle 60% of the shops.

Exercise 1.2 | Q 10 | Page 16

In a particular factory, workers produce various types of output units.
The following distribution was obtained.

 Output units Produced No. of workers 70 – 74 40 75 – 79 45 80 – 84 50 85 – 89 60 90 – 94 70 95 – 99 80 100 – 104 100

Find the percentage of workers who have produced less than 82 output units.

Exercise 1.3 [Pages 18 - 20]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 1 Partition Values Exercise 1.3 [Pages 18 - 20]

Exercise 1.3 | Q 1 | Page 18

The following table gives frequency distribution of marks of 100 students in an examination.

 Marks 15 –20 20 – 25 25 – 30 30 –35 35 –  40 40 – 45 45 – 50 No. of students 9 12 23 31 10 8 7

Determine D6, Q1, and P85 graphically.

Exercise 1.3 | Q 2 | Page 18

The following table gives the distribution of daily wages of 500 families in a certain city.

 Daily wages No. of families Below 100 50 100 – 200 150 200 – 300 180 300 – 400 50 400 – 500 40 500 – 600 20 600 above 10

Draw a ‘less than’ ogive for the above data. Determine the median income and obtain the limits of income of central 50% of the families.

Exercise 1.3 | Q 3 | Page 19

From the following distribution, determine median graphically.

 Daily wages (in ₹) No. of employees Above 300 520 Above 400 470 Above 500 399 Above 600 210 Above 700 105 Above 800 45 Above 900 7
Exercise 1.3 | Q 4. (i) | Page 19

The following frequency distribution shows the profit (in ₹) of shops in a particular area of city:

 Profit per shop (in ‘000) No. of shops 0 – 10 12 10 – 20 18 20 – 30 27 30 – 40 20 40 – 50 17 50 – 60 6

Find graphically The limits of middle 40% shops.

Exercise 1.3 | Q 4. (ii) | Page 19

The following frequency distribution shows the profit (in ₹) of shops in a particular area of city:

 Profit per shop (in ‘000) No. of shops 0 – 10 12 10 – 20 18 20 – 30 27 30 – 40 20 40 – 50 17 50 – 60 6

Find graphically the number of shops having profile less than 35,000 rupees.

Exercise 1.3 | Q 5 | Page 19

The following is the frequency distribution of overtime (per week) performed by various workers from a certain company.

Determine the values of D2, Q2, and P61 graphically.

 Overtime(in hours) Below 8 8 – 12 12 – 16 16 – 20 20 – 24 24 and above No. of workers 4 8 16 18 20 14
Exercise 1.3 | Q 6 | Page 19

Draw ogive for the following data and hence find the values of D1, Q1, P40.

 Marks less than 10 20 30 40 50 60 70 80 90 No. of students 4 6 24 46 67 86 96 99 100
Exercise 1.3 | Q 7 | Page 19

The following table shows the age distribution of head of the families in a certain country. Determine the third, fifth and eighth decile of the distribution graphically.

 Age of head of family (in years) Numbers (million) Under 35 46 35 – 45 85 45 – 55 64 55 – 65 75 65 – 75 90 75 and Above 40
Exercise 1.3 | Q 8 | Page 19

The following table gives the distribution of females in an Indian village. Determine the median age of graphically.

 Age group No. of females(in ‘000) 0 – 10 175 10 – 20 100 20 – 30 68 30 – 40 48 40 – 50 25 50 – 60 50 60 – 70 23 70 – 80 8 80 – 90 2 90 – 100 1
Exercise 1.3 | Q 9 | Page 19

Draw ogive for the Following distribution and hence find graphically the limits of weight of middle 50% fishes.

 Weight of fishes (in gms) 800 – 890 900 – 990 1000 – 1090 1100 –  1190 1200 – 1290 1300 –1390 1400 – 1490 No. of fishes 8 16 20 25 40 6 5
Exercise 1.3 | Q 10 | Page 20

Find graphically the values of D3 and P65 for the data given below:

 I.Q of students 60 – 69 70 – 79 80 – 89 90 – 99 100 – 109 110 – 119 120 – 129 No. of students 20 40 50 50 20 10 10
Miscellaneous Exercise 1 [Pages 20 - 22]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 1 Partition Values Miscellaneous Exercise 1 [Pages 20 - 22]

Miscellaneous Exercise 1 | Q 1 | Page 20

The data gives number of accidents per day on a railway track. Compute Q2, P17, and D7.

4, 2, 3, 5, 6, 3, 4, 1, 2, 3, 2, 3, 4, 3, 2.

Miscellaneous Exercise 1 | Q 2 | Page 20

The distribution of daily sales of shoes (size-wise) for 100 days from a certain shop is as follows:

 Size of shoes 2 4 3 5 7 6 8 No. of days 14 20 13 19 13 13 8

Compute Q1, D2, and P95.

Miscellaneous Exercise 1 | Q 3 | Page 20

Ten students appeared for a test in Mathematics and Statistics and they obtained the marks as follows:

 Sr. No. 1 2 3 4 5 6 7 8 9 10 Marks in Mathematics 42 38 36 32 23 25 35 37 25 23 Marks in Statistics 22 26 29 34 50 45 23 28 32 36

If the median will be the criteria, in which subject, the level of knowledge of the students is higher?

Miscellaneous Exercise 1 | Q 4 | Page 21

In the frequency distribution of families given below, the number of families corresponding to expenditure group 2000 - 4000 is missing from the table. However value of 25th percentile is 2880. Find the missing frequency.

 Weekly Expenditure (₹1000) 0 – 2 2 – 4 4 – 6 6 – 8 8 – 10 No. of families 14 ? 39 7 15
Miscellaneous Exercise 1 | Q 5 | Page 21

Calculate Q1, D6, and P15 for the following data:

 Mid value 25 75 125 175 225 275 Frequency 10 70 80 100 150 90
Miscellaneous Exercise 1 | Q 6 | Page 21

Daily income for a group of 100 workers are given below:

 Daily income (in₹) 0 – 50 50 – 100 100 – 150 150 – 200 200 – 250 No. of persons 7 ? 25 30 ?

P30 for this group is ₹ 110. Calculate the missing frequencies.

Miscellaneous Exercise 1 | Q 7 | Page 21

The distribution of a sample of students appearing for a C.A. examination is:

 Marks 0 – 100 100 – 200 200 – 300 300 – 400 400 – 500 500 – 600 No. of students 130 150 190 220 280 130

Help C.A. institute to decide cut-off marks for qualifying an examination when 3% of students pass the examination.

Miscellaneous Exercise 1 | Q 8 | Page 21

Determine graphically the value of median, D3, and P35 for the data given below:

 Class 10 – 15 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40 40 – 45 Frequency 8 14 8 25 15 14 6
Miscellaneous Exercise 1 | Q 9 | Page 21

The I.Q. test of 500 students of a college is as follows:

 I.Q. 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90 90 – 100 Number of students 41 52 64 180 67 45 40 11

Find graphically the number of students whose I.Q. is more than 55 graphically.

Miscellaneous Exercise 1 | Q 10 | Page 21

Draw an ogive for the following distribution. Determine the median graphically and verify your result by mathematical formula.

 Height (in cms.) No. of students 145 − 150 2 150 − 155 5 155 − 160 9 160 − 165 15 165 − 170 16 170 − 175 7 175 − 180 5 180 − 185 1
Miscellaneous Exercise 1 | Q 11 | Page 21

In a group of 25 students, 7 students failed and 6 students got distinction and the marks of the remaining 12 students are 61, 36, 44, 59, 52, 56, 41, 37, 39, 38, 41, 64. Find the median marks of the whole group.

Miscellaneous Exercise 1 | Q 12 | Page 21

The median weight of a group of 79 students is found to be 55 kg. 6 more students are added to this group whose weights are 50, 51, 52, 59.5, 60, 61 kg What will be the value of median of the combined group if the lowest and the highest weights were 53 kg and 59 kg respectively?

Miscellaneous Exercise 1 | Q 13 | Page 22

The median of the following incomplete table is 92. Find the missing frequencies:

 C.I. 30 – 50 50 – 70 70 – 90 90 – 110 110 – 130 130 – 150 Total f 6 ? 18 20 ? 10 80
Miscellaneous Exercise 1 | Q 14 | Page 22

A company produces tables which are packed in batches of 100. An analysis of the defective tubes in different batches has received the following information:

 No. of defective tubes Less than 5 5 – 9 10 – 14 15 – 9 20 – 24 25 – 29 30 and above No. of tubes 45 51 84 39 20 8 4

Estimate the number of defective tubes in the central batch.

Miscellaneous Exercise 1 | Q 15 | Page 22

In a college, there are 500 students in junior college, 5% score less than 25 marks, 68 score from 26 to 30 marks, 30% score from 31 to 35 marks, 70 score from 36 to 40 marks, 20% score from 41 to 45 marks and the rest score 46 and above marks. What is the median marks?

Miscellaneous Exercise 1 | Q 16 | Page 22

Draw a cumulative frequency curve more than type for the following data and hence locate Q1 and Q3. Also, find the number of workers with daily wages
(i) Between ₹ 170 and ₹ 260
(ii) less than ₹ 260

 Daily wages more than (₹) 100 150 200 250 300 350 400 450 500 No. of workers 200 188 160 124 74 49 31 15 5
Miscellaneous Exercise 1 | Q 17 | Page 22

Draw ogive of both the types for the following frequency distribution and hence find median.

 Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90 90 – 100 No. of students 5 5 8 12 16 15 10 8 5 2
Miscellaneous Exercise 1 | Q 18 | Page 22

Find Q1, D6, and P78 for the following data:

 C.I. 8 – 8.95 9 – 9.95 10 – 10.95 11 – 11.95 12 – 12.95 f 5 10 20 10 5
Miscellaneous Exercise 1 | Q 19 | Page 22
 Weight (kg) 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 65 –70 70 – 75 75 – 80 No. of person 4 15 20 30 20 10 8 4

For above data, find all quartiles and number of persons weighing between 57 kg and 72.

Miscellaneous Exercise 1 | Q 20 | Page 22

For the following data showing weights of 100 employees, find the maximum weight of the lightest 25% of employees.

 Weight (kg) 45 – 50 50 – 55 55 – 60 60 – 65 65 – 70 70 – 75 75 – 80 No. of employees 6 8 15 26 20 14 11

## Chapter 1: Partition Values

Exercise 1.1Exercise 1.2Exercise 1.3Miscellaneous Exercise 1

## Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 1 - Partition Values

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