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 | 11 - 13 | 13 - 15 | 15 - 17 | 17 - 19 | 19 - 21 | 21 - 23 | 23 - 25 |
| Number of workers | 7 | 6 | 9 | 13 | f | 5 | 4 |
The class mark (\(x_i\)) for each interval is calculated using the formula:
Class mark \((x_i)\) = \(\frac {\text{Upper \,limit + Lower \,limit}}{2}\)
The mean pocket allowance is given.
With an assumed mean of 18 (a), \(d_i\) and \(f_id_i\) are computed as follows.
| Daily pocket allowance (in Rs) | Number of children (\(f_i\)) | Class mark \(\bf{x_i}\) | \(\bf{d_i = x_i -150}\) | \(\bf{f_id_i}\) |
11 - 13 | 7 | 12 | -138 | -966 |
13 - 15 | 6 | 14 | -136 | -816 |
15 - 17 | 9 | 16 | -134 | -1206 |
17 - 19 | 13 | 18 | -132 | -1716 |
19 - 21 | \(f\) | 20 | -130 | -130\(f\) |
21 - 23 | 5 | 22 | -128 | -640 |
23 - 25 | 4 | 24 | -126 | -504 |
Total | \(\sum f_i\) = 44 + \(f\) |
|
| -130\(f\) - 5846 |
From the table, we have:
\(\sum f_i = 44 +f\)
\(\sum f_id_i = -130f - 5846\)
The mean is calculated as:
\(\overset{-}{x} = a + (\frac{\sum f_id_i}{\sum f_i})\)
18 = 18 + \((\frac{-130f - 5846}{44 + f})\)
0 = \(\frac{-130f - 5846}{44 + f}\)
-130\(f\) - 5846 = 0
-130\(f\) = 5846
\(f\) = -45
Therefore, the missing frequency f is -45.
A survey was conducted by a group of students as a part of their environment awareness programme, 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 plants | 0 − 2 | 2 − 4 | 4 − 6 | 6 − 8 | 8 − 10 | 10 − 12 | 12 − 14 |
| Number of houses | 1 | 2 | 1 | 5 | 6 | 2 | 3 |
Which method did you use for finding the mean, and why?
Consider the following distribution of daily wages of 50 workers of a factory
| Daily wages (in Rs) | 500 - 520 | 520 -540 | 540 - 560 | 560 - 580 | 580 -600 |
| Number of workers | 12 | 14 | 8 | 6 | 10 |
Find the mean daily wages of the workers of the factory by using an appropriate method.
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 heartbeats per minute | 65 - 68 | 68 - 71 | 71 - 74 | 74 - 77 | 77 - 80 | 80 - 83 | 83 - 86 |
| Number of boxs | 2 | 4 | 3 | 8 | 7 | 4 | 2 |
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 heartbeats per minute | 50-52 | 53-55 | 56-58 | 59-61 | 62-64 |
| Number of boxs | 15 | 110 | 135 | 115 | 25 |
Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?