Question

Find the mean, median and mode of the following data:

Class	0 – 50	50 – 100	100 – 150	150 – 200	200 – 250	250 – 300	300 - 350
Frequency	2	3	5	6	5	3	1

 

Answer 1

To find the mean let us put the data in the table given below:

Class	Frequency `(f_i)`	Class mark `(x_i)`	`f_i x_i`
0 – 50	2	25	50
50 – 100	3	75	225
100 – 150	5	125	625
150 – 200	6	175	1050
200 – 250	5	225	1125
250 – 300	3	275	825
300 – 350	1	325	325
Total	`Ʃ f_i `= 25		`Ʃ f_i x_i` = 4225

Mean =`( sum _i f_i x_i )/(sum _ i f_ i)`

           =`4225/25`

           = 169
Thus, mean of the given data is 169.

Now, to find the median let us put the data in the table given below:

Class	Frequency `(f_i)`	Cumulative Frequency (cf)
0 – 50	2	2
50 – 100	3	5
100 – 150	5	10
150 – 200	6	16
200 – 250	5	21
250 – 300	3	24
300 – 350	1	25
Total	`N = Σ f_i = 25`

Now, N = 25 ⇒`N/2 = 12.5`

The cumulative frequency just greater than 12.5 is 16 and the corresponding class is 150 – 200.
Thus, the median class is 150 – 200.
∴ l = 150, h = 50, N = 25, f = 6 and cf = 10.
Now,
Median = l +`((N/2 - cf)/f) xx h`

                = 150`((122.5-10)/6) xx 50` 

               = 150 + 20.83
               = 170.83
Thus, the median is 170.83.
We know that,
Mode = 3(median) – 2(mean)
            = 3 × 170.83 – 2 × 169
           = 512.49 – 338
           = 174.49
Hence, Mean = 169, Median = 170.83 and Mode = 174.49