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Question
Find the mean (correct to one place of decimal) by using short-cut method.
|
x |
40 |
41 |
43 |
45 |
46 |
49 |
50 |
|
f |
14 |
28 |
38 |
50 |
40 |
20 |
10 |
Solution
Let the assumed mean A = 45
| x | f | d = x – a = x – 45 | fd |
| 40 | 14 | –5 | –70 |
| 41 | 28 | –4 | –112 |
| 43 | 38 | –2 | –76 |
| A = 45 | 50 | 0 | 0 |
| 46 | 40 | 1 | 40 |
| 49 | 20 | 4 | 80 |
| 50 | 10 | 5 | 50 |
| Σf = 200 | Σfd = –88 |
∴ Mean = `A + (Σfd)/(Σf)`
= `45 + ((-88))/200`
= `45 - 11/25`
= `(1125 - 11)/25`
= `1114/25`
= 44.6
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