Mathemerize

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 …

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 : Read More »

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 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. Read More »

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 …

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. Read More »

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 …

Find the average expenditure which is being done by the maximum number of manual workers. Read More »

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 data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetime of the components Read More »

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 shows the ages of the patients admitted in a hospital. Find the mode of the given data. Read More »

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 %) …

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

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 (\(f_i\)) …

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. Read More »

Question : Concentration of \(SO_2\) (in ppm) Frequency 0.00 – 0.04 4 0.04 – 0.08 9 0.08 – 0.12 9 0.12 – 0.16 2 0.16 – 0.20 4 0.20 – 0.24 2 Solution : Let the assumed mean a = 0.10 Concentration of \(SO_2\) (in ppm) Frequency (\(f_i\)) Mid – Value (\(x_i\)) \(u_i\) = \(x_i …

To find out concentration of \(SO_2\) in the air (in parts per million, i.e. ppm), the data was collected for 30 localities in a certain city and is presented below. Find the mean concentration of \(SO_2\) in the air. Read More »

Question : Daily expenditure (in Rupees) 100 – 150 150 – 200 200 – 250 250 – 300 300 – 350 Number of households 4 5 12 2 2 Solution : Let the assumed mean, A = 225, class size, h = 50 So, \(u_i\) = \(x_i – A\over h\) = \(x_i – 225\over 50\) …

The table below shows expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method. Read More »