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:

= 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:

Now, N = 100 ⇒ \(\frac{N}2\) = 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 c f = 38. 

Now,

= 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