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**NCERT TEXTBOOK QUESTIONS SOLVED****Page No. 275****EXERCISE 14.2**

**Q 1. The following table shows the ages of the patients admitted in a hospital during a year:****Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.****Sol. ****Mode:**

Here, the highest frequency is 23.

The frequency 23 corresponds to the class interval 35 âˆ’ 45.

âˆ´ The modal class is 35 âˆ’ 45

Now, Class size (h) = 10

Lower limit (l) = 35 Frequency of the modal class (f_{1}) = 23

Frequency of the class preceding the modal class f_{0} = 21

Frequency of the class succeeding the modal class f_{2} = 14**Mean**

Let assumed mean a = 40

âˆµ h = 10

âˆ´ Required mean = 35.37 years.**Q 2. The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:****Determine the modal lifetimes of the components.****Sol.** Here, the highest frequency = 61.

âˆµ The frequency 61 corresponds to class 60 âˆ’ 80

âˆ´ The modal class = 60 âˆ’ 80

âˆ´ We have: l = 60

h = 20

f_{1} = 61

f_{0} = 52

f_{2} = 38

Thus, the required modal life times of the components are 65.625 hours.**Q 3. The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:****Sol. Mode: **

âˆµ The maximum number of families 40 have their total monthly expenditure is in interval 1500âˆ’2000.

âˆ´ Modal class is 1500âˆ’2000.

l = 1500, h = 500

f_{1} = 40, f_{0} = 24

f_{2} = 33

Thus, the required modal monthly expenditure of the families is Rs 1847.83.**Mean: **Let assumed mean (a) = 3250

âˆµ h = 500

âˆ´ We have the following table:

Thus, the mean monthly expenditure = Rs 2662.50.**Page No. 276****Q 4. The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.****Sol. Mode: **

Since the class 30 âˆ’ 35 has the greatest frequency and h = 5

l = 30

f_{1} = 10

f_{0} = 9

f_{2} = 3

Mean:

Let the assumed mean (a) = 37.5

Since, h = 5

âˆ´ We have the following table:

**Q 5. The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.****Find the mode of the data.****Sol. **The class 4000âˆ’5000 has the highest frequency i.e., 18

âˆ´ h = 1000

l = 4000

f_{1} = 18

f_{0} = 4

f_{2} = 9

Now,

Thus, the required mode is 4608.7.**Q 6. A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:****Sol**. âˆµ The class 40 âˆ’ 50 has the maximum frequency i.e., 20

âˆ´ f_{1} = 20,

f_{0} = 12,

f_{2} = 11 and h = 10

Also

l = 40

= 40 + 4.7 = 44.7

Thus, the required mode is 44.7

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