Question

A hockey player has scored following number of goals in 9 matches. 5, 4, 0, 2, 2, 4, 4, 3, 3. Find the mean, median and mode of the data.

Answer 1

Given Observations = 5,4,0,2,2,4,4,3,3

No.of observations = 9

(i)

We know that

Mean
= sum of observations/ no.of observations
= 5+4+0+2+2+4+4+3+3 /9
=27/9
=3

So mean = 3

(ii) we know that median is the central or middle value of a series..

Given series
5,4,0,2,2,4,4,3,3

arrange it in either ascending or descending order

Ascending order - 0,2,2,3,3,4,4,4,5
The middle value of the above series
-0,2,2,3,(3),4,4,4,5

So median is '3'

(iii) Weknow that Mode is the Most repeated value in the series..

Given series 5,4,0,2,2,4,4,3,3
Most repeated value in the above series is 4 (3 times)

so '4' is the mode

Answer 2

Few Formulas,

$mean \: \: = \frac{sum \: \: of \: \: observations}{total \: \: number \: \: of \: observations}$

$median \: \: = \frac{( \frac{n + 1}{2}) th \: \: observation}{2} \\ \\ \\ mode \: = most \: \: repeated \: \: observation$


××××××××××××××××××××××××××


1): Mean = { 5 + 4 + 0 + 2 + 2 + 4 + 4 + 3 + 3 } ÷ { 9 }



=> Mean = 27 ÷ 9

=> Mean = 3




2): Arrange in Ascending order,


0, 2, 2, 3, 3, 4, 4, 4, 5


Median = { ( 9 + 1 )th observation }÷2

Median = { 10th observation }÷2

Median = 5th observation

Median = 3



3): Mode = 4