PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoIn the previous topic, we have learnt how to find the mean using the direct method. Consider if the data is very large and finding the products of the observations and then adding them becomes tedious and also it may result in errors. To avoid such complications, let us use the assumed mean method to find the mean of grouped frequency.
Steps:
1. Calculate the midpoint of the class interval and name it as x.
2. From the data of x, choose any value(preferably in the middle) as the assumed mean(A).
3. Determine the deviation d=x-A for each of the class.
4. Multiply the deviation and frequency of each class interval and name it as fd.
5. Find the values \sum fd and \sum f.
6. Calculate the mean by applying the formula \overline X = A + \frac{\sum fd}{\sum f}
Example:
Find the mean of the following frequency distribution:
| Class interval | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |
| Frequency | 23 | 15 | 10 | 28 | 5 | 7 | 11 |
Solution:
Let the assumed mean be A = 45.
| Class interval | Frequency (f) | Midpoint (x) | Deviation d = x - A | fd |
| 10 - 20 | 23 | 15 | -30 | -690 |
| 20 - 30 | 15 | 25 | -20 | -300 |
| 30 - 40 | 10 | 35 | -10 | -100 |
| 40 - 50 | 28 | 45 | 0 | 0 |
| 50 - 60 | 5 | 55 | 50 | 250 |
| 60 - 70 | 8 | 65 | 20 | 160 |
| 70 - 80 | 11 | 75 | 30 | 330 |
| Total | \sum f = 100 | \sum fd = -350 |
We know that the mean of grouped data using the assumed mean method can be determined using the formula \overline X = A + \frac{\sum fd}{\sum f}
Substituting the known values in the above formula, we get:
\overline X = 45 + (\frac{-350}{100})
\overline X = 45 - 3.5
\overline X = 41.5
Therefore, the mean of the given data is 41.5.
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