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Question
Find the arithmetic mean (correct to the nearest whole number) by using step-deviation method.
| x | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| f | 20 | 43 | 75 | 67 | 72 | 45 | 39 | 9 | 8 | 6 |
Solution
Let the assumed mean = 30
|
x |
f |
d = x – A A = 30 |
`bb(t = (x - A)/i` `bb(= (x - 30)/5)` |
ft |
| 5 | 20 | –25 | –5 | –100 |
| 10 | 43 | –20 | –4 | –172 |
| 15 | 75 | –15 | –3 | –225 |
| 20 | 67 | –10 | –2 | –134 |
| 25 | 72 | –5 | –1 | –72 |
| 30 | 45 | 0 | 0 | 0 |
| 35 | 39 | 5 | 1 | 39 |
| 40 | 9 | 10 | 2 | 18 |
| 45 | 8 | 15 | 3 | 24 |
| 50 | 6 | 20 | 4 | 24 |
| Σf = 384 | Σft = –598 |
By step deviation method, we have
Mean = `A + (Σft)/(Σf) xx i`
= `(30 + (598) xx 5)/384`
= `30 + (-598)/384 xx 5`
= 30 – 7.79
= 22.21
= 22 (appx.) [To nearest whole number]
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