Class X
Statistics Exercise 14.2
QUESTION 1. The following table shows the ages of the patients admitted in a hospital during a year:
Sol. Mode:
Here, the highest frequency is 23.
The frequency 23 corresponds to the class interval 35 – 45.
The modeal class is 35 – 45 Now, Class size (h) = 10
Lower limit (l) = 35
Frequency of the modal class (f1) = 23
Frequency of the class preceding the modal class
f0 = 21
Frequency of the class succeeding the modal class
f2 = 14
Mode = 
= 36.8 years (approx.)
Mean
Let assumed mean a = 40
h = 10
Required mean = 35.37 years.Class X Statistics Exercise 14.2
QUESTION 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.
The frequency 61 corresponds to class 60 – 80
The modal class = 60 – 80
We have: l = 60 h = 20
f1 = 61
f0 = 52
f2 = 38
Mode = 
= 65.625 hours.
Thus, the required modal life times of the components is 65.625 hours.
Class X Statistics Exercise 14.2
QUESTION 3. The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly ependiture of the families. Also, the mean monthly expenditure:
Sol. Mode:
The maximum number of families 40 have their total monthly expenditure is in interval 1500 – 2000. 
Modal class is 1500 – 2000.
I = 1500, h = 500
f1 = 40, f0 = 24
f2 = 33
Mode = 
Thus, the required modal monthly expenditure of the families is Rs. 1847.83.
Mean: Let assumed mean (a) = 3250
h = 500
We have the following table:
= 2662.5
Thus, the mean monthly expenditure = Rs. 2662.50.
QUESTION 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 – 35 has the greatest frequency and h = 5
l = 30
f1 = 10
f0 = 9
f2 = 3
Mode = 
= 30 + 0.625 = 30.6 (approx).
Mean:
Let the assumed mean (a) = 37.5
Since, h = 5
We have the following table:
Class X Statistics Exercise 14.2
QUESTION 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 4000–5000 has the highest frequency i.e., 18
h = 1000 l = 4000
f1 = 18
f0 = 4
f2 = 9
Now, Mode = 
= 4000 + 608.695
= 4608.7 (approx.)
Thus, the required mode is 4608.7.
QUESTION 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. 
The class 40 – 50 has the maximum frequency i.e., 20
The class 40 – 50 has the maximum frequency i.e., 20
f1 = 20, f0 = 12, f2 = 11 and h = 10 Also l = 40
Mode = 
= 40 + 4.7 = 44.7