Question

For the data 11, 15, 17, x + 1, 19, x – 2, 3 if the mean is 14, find the value of x. Also find the mode of the data

Answer 1

Arithmetic mean = `"Sum of the observation"/"Number of observation"`

14 = `(11 + 15 + 17 + x  + 1 + 19 + x - 2 + 3)/7`

14 = `(2x +  64)/7`

∴ 2x + 64 = 14 × 7

2x = 98 – 64

2x = 34

x = `34/2`

= 17

The given numbers are 11, 15, 17, 18, 19, 15 and 3

15 occuring two times

∴ Mode = 15

The value of x = 17 and mode = 15