## 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 :

Question : Number of cars 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 Frequency 7 14 13 12 20 11 15 8 Solution : The class (40 – 50) has the maximum frequency frequency. Therefore, this is the modal …

## The given distribution shows the number of runs scored by some batsmen of the world in one-day international cricket matches. Find the mode of the data.

Question : Runs scored Number of batsmen 3000 – 4000 4 4000 – 5000 18 5000 – 6000 9 6000 – 7000 7 7000 – 8000 6 8000 – 9000 3 9000 – 10000 1 10000 – 11000 1 Solution : The class (4000 – 5000) has the maximum frequency. Therefore, this is the modal …

## The following distribution gives the step-wise teacher-student ration in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Question : Number of students per teacher Number of states/U.T. 15 – 20 3 20 – 25 8 25 – 30 9 30 – 35 10 35 – 40 3 40 – 45 0 45 – 50 0 50 – 55 2 Solution : The class (30 – 35) has the maximum frequency. Therefore, this …

## Find the average expenditure which is being done by the maximum number of manual workers.

Question : Expenditure (in Rs) 1000 – 1500 1500 – 2000 2000 – 2500 2500 – 3000 3000 – 3500 3500 – 4000 4000 – 4500 4500 – 5000 Manual workers (frequency) 24 40 33 28 30 22 16 7 Solution : The class (1500 – 2000) has maximum frequency i.e. 40, therefore this is …

## The following data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetime of the components

Question : Lifetimes (in hours) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120 Frequency 10 35 52 61 38 29 Solution : The following (60 – 80) has the maximum frequency. Therefore, this is the modal class. Here, l = 60, h = 20, $$f_1$$ …

## The following table shows the ages of the patients admitted in a hospital. Find the mode of the given data.

Question : Age (in years) 5 – 15 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65 No. of cases 6 11 21 23 14 5 Solution : The class (35 – 45) has maximum frequency, i.e. 23 therefore this is the modal class. Lower limit of the modal …

## The following table gives the literacy rate (in percentage) o f 35 cities. Find the mean literacy rate.

Question : Literacy rate (in %) 45 – 55 55 – 65 65 – 75 75 – 85 85 – 95 Number of cities 3 10 11 8 3 Solution : Let the assumed mean, A = 70 and class size, h = 10 So, $$u_i$$ = $$x_i – 70\over 10$$ Literacy rate (in %) …

## A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Question : Number of days 0 – 6 6 – 10 10 – 14 14 – 20 20 – 28 28 – 38 38 – 40 Number of students 11 10 7 4 4 3 1 Solution : Here, the class size varies, and $$x_i$$’s are small, Number of days Mid-Value ($$x_i$$) Number Students ($$f_i$$) …