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Mean of Grouped Data using Step Deviation Method
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The arithmetic mean in a measure of central tedency and is popularlyknown as mean. Arithmetic mean is obtained by dividing the sum of the values of all items of a series by the number of items of that series. Normally, arithmetic mean is denoted by $\bar X$ which is red as '$X$ bar'. It can be computed for unclassified or ungrouped data or individual series as well as classified or grouped data or discrete or continuous series.
From the following data calculate arithmentic mean.
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
|---|---|---|---|---|---|---|
| No. of students | 10 | 20 | 30 | 50 | 40 | 30 |
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A
$35$
💡 Explanation:
b'Let us take assumed mean $=$ 45
Calculation of deviations from assumed mean
| Marks | No. of | (X-45)/10 | ||
|---|---|---|---|---|
| X | m | students f | d | fd |
| 0-10 | 5 | 10 | -4 | -40 |
| 10-20 | 15 | 20 | -3 | -60 |
| 20-30 | 25 | 30 | -2 | -60 |
| 30-40 | 35 | 50 | -2 | -50 |
| 40-50 | 45 | 40 | 0 | 0 |
| 50-60 | 55 | 30 | +1 | 30 |
N $=$180 +9 $\sum fd = $-180
Mean $A \displaystyle + \frac{\sum fd}{N} \times c = 45+ \frac{-180 \times 10}{180} = 35$'