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Question
The table below shows the salaries of 280 persons :
| Salary (In thousand Rs) | No. of Persons |
| 5 – 10 | 49 |
| 10 – 15 | 133 |
| 15 – 20 | 63 |
| 20 – 25 | 15 |
| 25 – 30 | 6 |
| 30 – 35 | 7 |
| 35 – 40 | 4 |
| 40 – 45 | 2 |
| 45 – 50 | 1 |
Calculate the median salary of the data.
Solution
| Salary (In thousand Rs) | Frequency | CF |
| 5 – 10 | 49 | 49 |
| 10 – 15 | 133 | 182 |
| 15 – 20 | 63 | 245 |
| 20 – 25 | 15 | 260 |
| 25 – 30 | 6 | 266 |
| 30 – 35 | 7 | 273 |
| 35 – 40 | 4 | 277 |
| 40 – 45 | 2 | 279 |
| 45 – 50 | 1 | 280 |
`N/2 = 280/2 = 140`
The cumulative frequency which is greater than and nearest to 140 is 182.
Median class = 10-15
We also have,
l (lower limit of median class) = 10
h (class size) = 5
n (number of observations) = 280
cf = (cumulative frequency of the class preceding the median class) = 49
f (frequency of median class) = 133
Median for grouped data is given by the formula :
Median = `l + ((n/2 - cf)/f) xx h`
where f is the frequency of median class and cf is the cumulative frequency of previous class.
Median = `10 + (140 - 49)/133 xx 5 = 13.42`
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