Find the median for the following data.
Observation367910Frequency8101598
Sum of frequency is 50 or ∑fi = 50 and calculate less than cumulative frequencies in the table.
observation (xi) frequency (fi) cumulative frequency (cfi)3 | 8 | 8 |
6 | 10 | 18 |
7 | 15 | 33 (Median Class) |
9 | 9 | 42 |
10 | 8 | 50 |
∑fi=50 |
Since, even number of observation so the median will be the average of
(n2)th = (502)th observation and (n2+1)th = (502+1)th observation i.e., average of 25th and 26th observations repectively.
The first 8 observations occurs 3 times, next 10 occurs times and next 15 occurs 7 times.
So, the 25th and 26th observation will be 7 and 7 respectively.
Average of 7 and 7 = 7 + 72 = 7
Thus, median of the given data is 7.