NCERT Solution: Statistics
Find the mean salary of 60 workers of a factory from the following table:
|
Salary (in Rs) |
Number of workers |
|
3000 |
16 |
|
4000 |
12 |
|
5000 |
10 |
|
6000 |
8 |
|
7000 |
6 |
|
8000 |
4 |
|
9000 |
3 |
|
1000 |
1 |
|
Total |
60 |
|
Salary (xi) |
Number of workers (fi) |
fixi |
| 3000 | 16 | 48000 |
| 4000 | 12 | 48000 |
| 5000 | 10 | 50000 |
| 6000 | 8 | 48000 |
| 7000 | 6 | 42000 |
| 8000 | 4 | 32000 |
| 9000 | 3 | 27000 |
| 10000 | 1 | 10000 |
| Total |
Σfi = 60 | Σfixi = 305000 |
= 5083.33
Therefore, mean salary of 60 workers is Rs 5083.33.
When any data has a few observations such that these are very far from the other observations in it, it is better to calculate the median than the mean of the data as median gives a better estimate of average in this case.
(i) Consider the following example - the following data represents the heights of the members of a family.
154.9 cm, 162.8 cm, 170.6 cm, 158.8 cm, 163.3 cm, 166.8 cm, 160.2 cm
In this case, it can be observed that the observations in the given data are close to each other. Therefore, mean will be calculated as an appropriate measure of central tendency.
(ii) The following data represents the marks obtained by 12 students in a test.
48, 59, 46, 52, 54, 46, 97, 42, 49, 58, 60, 99
In this case, it can be observed that there are some observations which are very far from other observations. Therefore, here, median will be calculated as an appropriate measure of central tendency.
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