Question

The marks of 20 students in a test were as follows:

2, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19 and 20.

Calculate:

1. the mean
2. the median
3. the mode 

Answer 1

Arranging the terms in ascending order: 

2, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20 

Number of terms = 20 

Σx = 2 + 6 + 8 + 9 + 10 + 11 + 11 + 12 + 13 + 13 + 14 + 14 + 15 + 15 + 15 + 16 + 16 + 18 + 19 + 20 = 257  

i. Mean = `(∑x)/(∑n) = 257/20 = 12.85` 

ii. Median = `(10^(th)  term + 11^(th)  term)/2`

= `(13 + 14)/2`

= `27/2`

= 13.5 

iii. Mode = 15 as it has maximum frequencies i.e. 3