NCERT Class XI Mathematics - Statistics - Solutions
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Question : 23
Total: 34
From the data given below state which group is more variable, A or B?
| Marks | Group A | Group B |
|---|---|---|
| 10 - 20 | 9 | 10 |
| 20 - 30 | 17 | 20 |
| 30 - 40 | 32 | 30 |
| 40 - 50 | 33 | 25 |
| 50 - 60 | 40 | 43 |
| 60 - 70 | 10 | 15 |
| 70 - 80 | 9 | 7 |
Solution:
For Group A :
Let assumed mean (A) = 45
Mean(
)
Standard deviation (σ 1
√ N Σ f i u i 2 − ( Σ f i u i ) 2
√ 150 × 342 − ( − 6 ) 2
√ 51300 − 36
=
For Group B :
Mean(
) 2
Standard deviation( σ 2 )
√ N Σ f i u i 2 − ( Σ f i u i ) 2
√ 150 × 366 − ( − 6 ) 2
√ 54900 − 36
=
The group which have greater S.D. is more variable. Thus group B is more variable.
| Marks | Mid values | | | | | ||
|---|---|---|---|---|---|---|---|
| 10 - 25 | 15 | 9 | - 3 | - 27 | 81 | ||
| 20 - 30 | 25 | 17 | - 2 | - 34 | 68 | ||
| 30 - 40 | 35 | 32 | - 1 | - 32 | 32 | ||
| 40 - 50 | 45 | 33 | 0 | 0 | 0 | ||
| 50 - 60 | 55 | 40 | 1 | 40 | 40 | ||
| 60 - 70 | 65 | 10 | 2 | 20 | 40 | ||
| 70 - 80 | 75 | 9 | 3 | 27 | 91 | ||
| 150 | - 6 | 342 |
Let assumed mean (A) = 45
Mean
Standard deviation (
=
For Group B :
| Marks | Mid values | | | | | ||
|---|---|---|---|---|---|---|---|
| 10 - 25 | 15 | 10 | - 3 | - 30 | 90 | ||
| 20 - 30 | 25 | 20 | - 2 | - 40 | 80 | ||
| 30 - 40 | 35 | 30 | - 1 | - 30 | 30 | ||
| 40 - 50 | 45 | 25 | 0 | 0 | 0 | ||
| 50 - 60 | 55 | 43 | 1 | 43 | 43 | ||
| 60 - 70 | 65 | 15 | 2 | 30 | 60 | ||
| 70 - 80 | 75 | 7 | 3 | 21 | 63 | ||
| 150 | - 6 | 366 |
Mean
Standard deviation
=
The group which have greater S.D. is more variable. Thus group B is more variable.
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