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Question
Calculate the median of the following sets of number:
1, 9, 10, 8, 2, 4, 4, 3, 9, 1, 5, 6, 2 and 4.
Solution
Arranging these numbers in ascending order,
1, 1, 2, 2, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10
Here N = 14
∴ `("N"/2)^"th"` term
= `(14/2)`
= 7th term
= 4
`("N" /2 + 1)^"th"`term
= 7 + 1
= 8th term
= 4
∴ Median
= `(4 + 4)/(2)`
= `(8)/(2)`
= 4
Or
Median = 4.
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Calculate the mean of the distribution given below using the shortcut method.
| Marks | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 | 61-70 | 71-80 |
| No. of students | 2 | 6 | 10 | 12 | 9 | 7 | 4 |
The following are the marks obtained by 70 boys in a class test:
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| 30 – 40 | 10 |
| 40 – 50 | 12 |
| 50 – 60 | 14 |
| 60 – 70 | 12 |
| 70 – 80 | 9 |
| 80 – 90 | 7 |
| 90 – 100 | 6 |
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| Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
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(i) Median
(ii) Mode
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| Frequency | 4 | 7 | 6 | 3 | 5 |
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| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| Frequency | 4 | 12 | 21 | 18 | 15 | 7 | 3 |
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