In a mathematics test given to $15$ students,the following marks (out of $100$) are recorded:
$41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60$
Find the mean,median,and mode of this data.
$41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60$
Find the mean,median,and mode of this data.
(N/A) The marks of $15$ students in the mathematics test are:
$41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60$
$1.$ Mean of data = (Sum of all observations) / (Total number of observations)
$= (41 + 39 + 48 + 52 + 46 + 62 + 54 + 40 + 96 + 52 + 98 + 40 + 42 + 52 + 60) / 15$
$= 822 / 15 = 54.8$
$2.$ Arranging the scores in ascending order:
$39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98$
Since the number of observations $n = 15$ (which is odd),the median is the value of the $((n+1)/2)^{\text{th}}$ observation.
Median = $((15+1)/2)^{\text{th}} = 8^{\text{th}}$ observation.
The $8^{\text{th}}$ observation is $52$.
$3.$ Mode is the observation with the maximum frequency.
Here,$52$ appears $3$ times,which is the highest frequency.
Therefore,the mode is $52$.
$41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60$
$1.$ Mean of data = (Sum of all observations) / (Total number of observations)
$= (41 + 39 + 48 + 52 + 46 + 62 + 54 + 40 + 96 + 52 + 98 + 40 + 42 + 52 + 60) / 15$
$= 822 / 15 = 54.8$
$2.$ Arranging the scores in ascending order:
$39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98$
Since the number of observations $n = 15$ (which is odd),the median is the value of the $((n+1)/2)^{\text{th}}$ observation.
Median = $((15+1)/2)^{\text{th}} = 8^{\text{th}}$ observation.
The $8^{\text{th}}$ observation is $52$.
$3.$ Mode is the observation with the maximum frequency.
Here,$52$ appears $3$ times,which is the highest frequency.
Therefore,the mode is $52$.
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