Question

In a maths test the following marks out of 100 are recorded for 15 students .find mean,mode,median. 41,39,48,52,46,62,54,40,96,52,98,40,42,52,60.​

Answer 1

mean=sum of observations/ no of observations

=41+39+48+52+46+62+54+40+96+52+98+40+42+52+60/15

=822/15

=54.8

median= middle observation=n+1/2=15+1/2=16/2=8th

median=40

mode = repeating observation=52

Answer 2

$\bold{To \: find \: mean }$

Given observations ➡ 41,39,48,52,46,62,54,40,96,52,98,40,42,52,60

Number of observations ➡ 15

$Mean = \frac{sum \: of \: observations}{number \: of \: observations}$

$= \frac{41 + 39 + 48 + 52 + 46 + 62 + 54 + 40 + 96 + 52 +98 + 40 + 42 + 52 + 60}{15}$

$Mean = \frac{822}{15}$

$Mean = 54.8$

$\boxed{Mean \: = \: 54.8}$

$\bold{To \: find \: median}$

Given observations ➡ 41,39,48,52,46,62,54,40,96,52,98,40,42,52,60

Number of observations ➡ 15 [odd]

Arrange the observations in ascending order➡

39,40,40,41,42,46,48,52,52,52,54,60,62,96,98

$Median = \frac{n + 1}{2}$

$Median = \frac{15 + 1}{2}$

$Median = \frac{16}{2}$

$Median = 8th \: observation$

$\boxed{Median \: = \: 52}$

$\bold{To \: find \: mode}$

The number which repeats frequently is known as the mode of the data.

Given observations ➡ 41,39,48,52,46,62,54,40,96,52,98,40,42,52,60

Arrange the observations in ascending order➡

39,40,40,41,42,46,48,52,52,52,54,60,62,96,98

$\boxed{Mode \: = \: 52}$