## Chapter 7 Statistics R.D. Sharma Solutions for Class 10th Math Exercise 7.4

1.Â Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:
715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719.

**Solution**

2. The following is the distribution of height of students of a certain class in a certain city:

Height (in cm): 160-162 163-165 166-168 169-171 172-174

No. of students:Â 15Â 118 142 127 18

Find the median height.Â

Height (in cm): 160-162 163-165 166-168 169-171 172-174

No. of students:Â 15Â 118 142 127 18

Find the median height.Â

**Solution**

3. Following is the distribution of I.Q. of loo students. Find the median I.Q.

I.Q.:Â Â 55-64Â 65-74Â 75-84Â 85-94Â 95-104Â 105-114Â 115-124Â 125-134Â 135-144

No of Students: 1Â 2Â 9Â 22Â 33Â 22Â 8Â 2Â 1

I.Q.:Â Â 55-64Â 65-74Â 75-84Â 85-94Â 95-104Â 105-114Â 115-124Â 125-134Â 135-144

No of Students: 1Â 2Â 9Â 22Â 33Â 22Â 8Â 2Â 1

**Solution**

4. Calculate the median from the following data:

Rent (in Rs.): 15-25 25-35 35-45 45-55 55-65 65-75 75-85 85-95

No. of Houses: 8Â 10Â 15Â 25Â 40Â 20Â 15Â 7Â

Rent (in Rs.): 15-25 25-35 35-45 45-55 55-65 65-75 75-85 85-95

No. of Houses: 8Â 10Â 15Â 25Â 40Â 20Â 15Â 7Â

**Solution**

5. Calculate the median from the following data:

Marks below: 10 20 30 40 50Â 60Â Â 70 80

No. of students: 15 35 60 84 96 127 198 250

Marks below: 10 20 30 40 50Â 60Â Â 70 80

No. of students: 15 35 60 84 96 127 198 250

**Solution**

6. Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Age in years:Â 0-10 10-20 20-30 30-40 40-50

No. of persons: 5Â 25Â ?Â 18Â 7

Age in years:Â 0-10 10-20 20-30 30-40 40-50

No. of persons: 5Â 25Â ?Â 18Â 7

**Solution**

7. The following table gives the frequency distribution of married women by age at marriage:

Calculate the median and interpret the results

**Solution**

8. The following table gives the distribution of the life time of 400 neon lamps:Â Â

Find the median life .

**Solution**

9. The distribution below gives the weight of 30 students in a class. Find the median weight of students:

Weight (in kg): 40-45 45-50 50-55 55-60 60-65 65-70 70-75

No. of students:Â 2Â 3Â 8Â 6Â 6Â 3Â 2

Weight (in kg): 40-45 45-50 50-55 55-60 60-65 65-70 70-75

No. of students:Â 2Â 3Â 8Â 6Â 6Â 3Â 2

**Solution**

10. Find the missing frequencies and the median for the following distribution if the mean is

1.46.

No. of accidents:Â 0Â 1Â 2Â 3Â Â 4Â 5Â Total

Frequency (No. of days): 46Â ?Â ?Â 25Â 10Â 5Â 200

**Solution**

11. An incomplete distribution is given below:

Variable: 10-20Â 20-30Â 30-40Â 40-50Â 50-60Â 60-70Â 70-80

Frequency: 12Â 30Â -Â 6Â 5 -Â 25Â Â 18

You are given that the median value is 46 and the total number of items is 230.

(i) Using the median formula fill up missing frequencies.

(ii) Calculate the AM of the completed distribution.

Variable: 10-20Â 20-30Â 30-40Â 40-50Â 50-60Â 60-70Â 70-80

Frequency: 12Â 30Â -Â 6Â 5 -Â 25Â Â 18

You are given that the median value is 46 and the total number of items is 230.

(i) Using the median formula fill up missing frequencies.

(ii) Calculate the AM of the completed distribution.

**Solution**

(i)

12. If the median of the following frequency distribution is 28.5 find the missing frequencies:

Class interval: 0-10 10-20 20-30 30-40 40-50 50-60 Total

Frequency:Â Â Â Â Â 5Â Â Â Â f 1Â Â Â 20Â Â Â Â 15Â Â Â f 2Â Â Â 5Â Â Â 60Â

(ii)Â

Class interval: 0-10 10-20 20-30 30-40 40-50 50-60 Total

Frequency:Â Â Â Â Â 5Â Â Â Â f 1Â Â Â 20Â Â Â Â 15Â Â Â f 2Â Â Â 5Â Â Â 60Â

Sol.

13. The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the data:Â

**Solution**Â

14. If the median of the following data is 32.5, find the missing frequencies.

Class interval: 0- 10Â 10-20Â 20-30Â 30-40Â 40-50Â 50-60Â 60-70Â Total

Frequency: f

Class interval: 0- 10Â 10-20Â 20-30Â 30-40Â 40-50Â 50-60Â 60-70Â Total

Frequency: f

_{1}Â 5Â 9Â 12Â f_{2}Â 3Â 2Â 40**Solution**

15. Compute the median for each of the following data:Â Â

(i)

**Solution**Â

(i)

(ii)

16. A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and

the following data was obtained:

Height in cmÂ Number of Girls

Less than 140Â Â 4

Less than 145Â 11

Less than 150Â 29

Less than 155Â 40

Less than 160Â 46

Less than l65Â Â 51

Find the median height.

**Solution**

To calculate the median height, we need to find the class intervals and their corresponding frequencies .

The given distribution being of thee less than type 140, 145, 150,â€¦..,165 give the upper limits of the corresponding class intervals. So, the classes should be below 140, 145, 150,â€¦.., 160, 165 observe that from the given distribution, we find that there are 4-girls with height less than 140 is 4. Now there are 4 girls with heights less than 140. Therefore, the number of girls with height in the interval 140, 145 is 11- 4=7, similarly. The frequencies of 145 150 is 29-11=18, for 150-155 it is 40-29=11, and so on so our frequencies distribution becomes.

17. A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons having age 18 years onwards but less than 60 years.

Age in yearsÂ Number of policy holders

Below 20Â Â 2

Below 25Â Â 6

Below 30Â Â 24

Below 35Â Â 45

Below 40Â Â 78

Below 45Â Â 89

Below 50Â Â 92

Below 55Â Â 98

Below 60Â Â 100

18. The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

Length (in mm): 118-126Â 127-135Â 136-144Â 145-153Â 154-162Â 163-171Â 172-180

No. of leaves:Â 3Â Â 5Â Â 9Â 12Â Â 5Â 4Â 2

Find the mean length of life.Â

Below 25Â Â 6

Below 30Â Â 24

Below 35Â Â 45

Below 40Â Â 78

Below 45Â Â 89

Below 50Â Â 92

Below 55Â Â 98

Below 60Â Â 100

**Solution**18. The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

Length (in mm): 118-126Â 127-135Â 136-144Â 145-153Â 154-162Â 163-171Â 172-180

No. of leaves:Â 3Â Â 5Â Â 9Â 12Â Â 5Â 4Â 2

Find the mean length of life.Â

**Solution**

19. An incomplete distribution is given as follows:

Variable: 0-10 10-20Â 20-30Â 30-40Â 40â€“50Â 50-60Â 60-70

Frequency: 10Â 20Â ?Â 40Â ?Â 25 15

You are given that the median value is 35 and the sum of all the frequencies is 170. Using

the median formula, fill up the missing frequencies.Â

**Solution**

20. The median of the distribution given below is 14.4 . Find the values of x and y , if the total frequency is 20.Â

Class intervalÂ : 0-6Â 6-12 12-18 18-24 24-30

Frequency :Â Â Â Â 4Â Â Â Â xÂ Â Â Â 5Â Â Â Â yÂ Â Â Â 1

**Solution**

21.Â The median of the following data is 50. Find the value of p and q , if the sum of all the frequencies is 90.Â

**Solution**