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Question
The following are the marks obtained by 70 boys in a class test:
| Marks | No. of boys |
| 30 – 40 | 10 |
| 40 – 50 | 12 |
| 50 – 60 | 14 |
| 60 – 70 | 12 |
| 70 – 80 | 9 |
| 80 – 90 | 7 |
| 90 – 100 | 6 |
Calculate the mean by:
Step-deviation method
Solution
Step-deviation method
|
Marks |
No. of boys |
Mid-value |
A = 65 |
fiui |
| 30 – 40 | 10 | 35 | –3 | –30 |
| 40 – 50 | 12 | 45 | –2 | –24 |
| 50 – 60 | 14 | 55 | –1 | –14 |
| 60 – 70 | 12 | A = 65 | 0 | 0 |
| 70 – 80 | 9 | 75 | 1 | 9 |
| 80 – 90 | 7 | 85 | 2 | 14 |
| 90 – 100 | 6 | 95 | 3 | 18 |
| Total | 70 | –27 |
Here A = 65 and h = 10
`barx = A + h xx (sumf_iu_i)/(sum f_i)`
= `65 +10 xx ((-27)/70)`
= 65 – 3.86
= 61.14
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