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Question 3

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

Daily Pocket Allowance(in c)11-1313-1515- 1717-1919-2121-2323-35
Number of children76913f54

Solution:

To find out the missing frequency, use the mean formula.

Given, mean $\overline{x}$ = 18

Class intervalNumber of children $(f_i)$Mid-point $(x_i)$$f_ix_i $
11-1371284
13- 1561484
15-17916144
17- 191318234
19-21f2020f
21- 23522110
23-2542496
Total$f_i$ = 44+fSum$ f_{i}x_i$ = 752+20f

The mean formula is

Mean = $\overline{x} = \dfrac{∑f_ix_i }{∑f_i}$

= $\dfrac{(752 + 20f)}{(44 + f)}$

Now substitute the values and equate to find the missing frequency (f)

18 = $\dfrac{(752 + 20f)}{(44 + f)}$

18(44 + f) = (752 + 20f)

792 + 18f = 752 + 20f

792 + 18f = 752 + 20f

792 – 752 = 20f – 18f

40 = 2f

f = 20

So, the missing frequency, f = 20.

Additional Questions

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

Number of heart beats per minute65-6868-7171- 7474-7777-8080-8383-86
Number of women2438742

Answer

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.

Number of mangoes50-5253-5556-5859- 6162-64
Number of boxes1511013511525

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Answer

The table below shows the daily expenditure on food of 25 households in a locality.

Daily expenditure(in c)100-150150-200200- 250250-300300-350
Number of households451222

Find the mean daily expenditure on food by a suitable method.

Answer

To find out the 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:

Concentration of $SO_2$ ( in ppm)Frequency
0.00 – 0.044
0.04 – 0.089
0.08 – 0.129
0.12 – 0.162
0.16 – 0.204
0.20 – 0.242

Find the mean concentration of $SO_2$ in the air.

Answer

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.

Number of days0-66-1010-1414- 2020-2828-3838-40
Number of students111074431

Answer

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

Literacy rate (in %)45-5555-6565-7575 -8585-98
Number of cities3101183

Answer

A survey was conducted by a group of students as a part of their environment awareness program, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

Number of Plants0-22-44-66-88 -1010-1212-14
Number of Houses1215623

Which method did you use for finding the mean, and why?

Answer

Consider the following distribution of daily wages of 50 workers of a factory.

Daily wages (in Rs.)500-520520-540540- 560560-580580-600
Number of workers12148610

Find the mean daily wages of the workers of the factory by using an appropriate method.

Answer

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

Daily Pocket Allowance(in c)11-1313-1515- 1717-1919-2121-2323-35
Number of children76913f54

Answer

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

Number of heart beats per minute65-6868-7171- 7474-7777-8080-8383-86
Number of women2438742

Answer
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