#### Chapters

## Chapter 1: Partition Values

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

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.

The heights (in cm) of 10 students are given below: 148, 171, 158, 151, 154, 159, 152, 163, 171, 145. Calculate Q_{1} and Q_{3} for above data.

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.

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 |

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 |

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.

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 |

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.

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.

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 |

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

Calculate D_{6} and P_{85} for the following data:

79, 82, 36, 38, 51, 72, 68, 70, 64, 63.

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 D_{8} and P_{90}.

Calculate 2^{nd} decide and 65^{th} 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 |

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

House rent (in ₹) |
11000 | 12000 | 13000 | 15000 | 14000 | 16000 | 17000 | 18000 |

No. of houses |
25 | 17 | 13 | 14 | 15 | 8 | 6 | 2 |

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.

Calculate D_{4} and P_{48} from the following data:

Mid value |
2.5 | 7.5 | 12.5 | 17.5 | 22.55 | Total |

Frequency |
7 | 18 | 25 | 30 | 20 | 100 |

Calculate D_{6 }and P_{20} 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 |

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 | ? |

D_{3} for this group is ₹1100 Calculate the missing frequencies.

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.

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.

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

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 D_{6}, Q_{1,} and P_{85} graphically.

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.

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 |

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.

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.

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

Determine the values of D_{2}, Q_{2,} and P_{61} 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 |

Draw ogive for the following data and hence find the values of D_{1}, Q_{1}, P_{40}.

Marks less than |
10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 |

No. of students |
4 | 6 | 24 | 46 | 67 | 86 | 96 | 99 | 100 |

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 |

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 |

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 |

Find graphically the values of D_{3} and P_{65} 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 |

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

The data gives number of accidents per day on a railway track. Compute Q_{2}, P_{17,} and D_{7}.

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

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 Q_{1}, D_{2,} and P_{95}.

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?

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 25^{th} 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 |

Calculate Q_{1}, D_{6,} and P_{15} for the following data:

Mid value |
25 | 75 | 125 | 175 | 225 | 275 |

Frequency |
10 | 70 | 80 | 100 | 150 | 90 |

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 | ? |

P_{30} for this group is ₹ 110. Calculate the missing frequencies.

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.

Determine graphically the value of median, D_{3,} and P_{35} 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 |

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.

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 |

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.

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?

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 |

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.

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?

Draw a cumulative frequency curve more than type for the following data and hence locate Q_{1} and Q_{3}. 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 |

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 |

Find Q_{1}, D_{6,} and P_{78} 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 |

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.

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

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

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 1 (Partition Values) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 1 Partition Values are Concept of Median, Partition Values, Quartiles, Deciles, Percentiles, Relations Among Quartiles, Deciles and Percentiles, Graphical Location of Partition Values.

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