Question

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

Marks obtained	25 - 35	35 – 45	45 – 55	55 – 65	65 – 75	75 - 85
No. of students	7	31	33	17	11	1

 

 

Answer 1

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

Marks obtained	Number of students `(f_i)`	Class mark `(x_i)`	`f_i x_i`
25 – 35	7	30	210
35 – 45	31	40	1240
45 – 55	33	50	1650
55 – 65	17	60	1020
65 – 75	11	70	770
75 – 85	1	80	80
Total	`Ʃ f_i` = 100		`Ʃ f_i x_i` = 4970

Mean =`(sum _i f_i x_i )/(sum _i f_i )`

          =`4970/100`

         = 49.7
Thus, mean of the given data is 49.7.
Now, to find the median let us put the data in the table given below:

Class	Frequency `(f_i)`	Cumulative Frequency (cf)
25 – 35	7	7
35 – 45	31	38
45 – 55	33	71
55 – 65	17	88
65 – 75	11	99
75 – 85	1	100
Total	`N = Σ f_i`= 100

Now, N = 100 ⇒`N/2 =50`
The cumulative frequency just greater than 50 is 71 and the corresponding class is 45 – 55.
Thus, the median class is 45 – 55.
∴ l = 45, h = 10, N = 100, f = 33 and cf = 38.
Now,

Median = l +`((N/2- cf)/f) xxh`

            `=45+((50-38)/33) xx 10`

            = 45 + 3.64
            = 48.64
Thus, the median is 48.64.
We know that,
Mode = 3(median) – 2(mean)
          = 3 × 48.64 – 2 × 49.70
          = 145.92 – 99.4
          = 46.52
Hence, Mean = 49.70, Median = 48.64 and Mode = 46.52