mathemerize

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 »

Question : Number of Mangoes 50 – 52 53 – 55 56 – 58 59 – 61 62 – 64 Number of Boxes 15 110 135 115 25 Solution : Here, the class intervals are formed by the exclusive method. If we make the data an inclusive one, the mid-values remain same. So there is …

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes. Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose ? Read More »

Question : Number of heart beats per minute 65 – 68 68 – 71 71 – 74 74 – 77 77 – 80 80 – 83 83 – 86 Number of women 2 4 3 8 7 4 2 Solution : Let assumed mean a = 75.5 Number of heart beats No. of women \(f_i\) …

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as follows. Find the mean heart beats per minute for these women, choosing a suitable method. Read More »

Question : Class Interval 11 – 13 13 – 15 15 – 17 17 – 19 19 – 21 21 – 23 23 – 25 Frequency 7 6 9 13 f 5 4 Solution : We have, Class Interval Mid-value (\(x_i\)) Frequency (\(f_i\)) \(f_ix_i\) 11 – 13 12 7 84 13 – 15 14 6 …

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is 18 rupees. Find the missing frequency f. Read More »