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The runs scored in a cricket match by 11 players is as follows:
6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Find the mean, mode and median of this data. Are the three same?
Given:
The runs scored in a cricket match by 11 players are as follows:
6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
To do:
We have to find the mean, mode and median of this data and whether the three are same.
Solution:
Total number of players$=11$
Scores of the players $=$6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Arranging the scores into ascending order, we get
6, 8, 10, 15, 15, 15, 50, 80, 100, 120
$\boxed{ \text { Mean }=\frac{ \text { Sum of all scores }}{ \text { Total number of players }}}$
$=\frac{6+8+10+15+15+15+50+80+100+120}{11}$
$=\frac{429}{11}$
$=39$
Thus, mean $=39$
Mode is the observation that occurs the highest number of times.
Here, $15$ occurs $3$ times in the given data.
$\therefore$ Mode $=15$
The arranged data is: 6, 8, 10,10, 15, 15, 15, 50, 80, 100, 120
Median is the middlemost observation of the given data
There are $11$ observations here. Thus the middle value is the 6th observation.
Median$=15$ [6th observation]
Therefore, Mean$=39$, Mode$=15$ and median$=15$
No, the mean, mode, and median are not the same.
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