The following table gives the daily income of 50 workers of a factory:
Daily income (in Rs.) | 100 - 120 | 120 - 140 | 140 - 160 | 160 - 180 | 180 - 200 |
Number of workers | 12 | 14 | 8 | 6 | 10 |
Find the mean, mode and median of the above data.
To find mean, we will solve by direct method:
DAILY INCOME (Rs.) | MID - POINT(xi) | NUMBER OF WORKERS(fi) | fixi |
100 - 120 | 110 | 12 | 1320 |
120 - 140 | 130 | 14 | 1820 |
140 - 160 | 150 | 8 | 1200 |
160 - 180 | 170 | 6 | 1020 |
180 - 200 | 190 | 10 | 1900 |
TOTAL | 50 | 7260 |
We have got
Σfi = 50 & Σfixi = 7260
∵ mean is given by
⇒ 
⇒ 
To find median,
Assume Σfi = N = Sum of frequencies,
h = length of median class,
l = lower boundary of the median class,
f = frequency of median class
and Cf = cumulative frequency
Lets form a table.
DAILY INCOME (Rs.) | NUMBER OF WORKERS(fi) | Cf |
100 - 120 | 12 | 12 |
120 - 140 | 14 | 12 + 14 = 26 |
140 - 160 | 8 | 26 + 8 = 34 |
160 - 180 | 6 | 34 + 6 = 40 |
180 - 200 | 10 | 40 + 10 = 50 |
TOTAL | 50 |
So, N = 50
⇒ N/2 = 50/2 = 25
The cumulative frequency just greater than (N/2 = ) 25 is 26, so the corresponding median class is 120 - 140 and accordingly we get Cf = 12(cumulative frequency before the median class).
Now, since median class is 120 - 140.
∴ l = 120, h = 20, f = 14, N/2 = 25 and Cf = 12
Median is given by,
⇒ 
= 120 + 18.57
= 138.57
And we know that,
Mode = 3(Median) – 2(Mean)
= 3(138.57) – 2(145.2)
= 415.71 – 290.4
= 125.31
Hence, mean is 145.2, median is 138.57 and mode is 125.31.