In a diagnostic test in mathematics given to students,the following marks (out of $100$) are recorded:
$46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44$
Which 'average' will be a good representative of the above data and why?
$46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44$
Which 'average' will be a good representative of the above data and why?
(B) The median is the best representative of the given data.
The recorded marks (out of $100$) are: $46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44$.
The median is a good representative because:
$(i)$ The mean is significantly influenced by extreme values (outliers) such as $11, 96,$ and $98$,which pull the average away from the central cluster of scores.
$(ii)$ The median provides a better measure of central tendency when the data set contains extreme values,as it represents the middle value of the ordered data set.
The recorded marks (out of $100$) are: $46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44$.
The median is a good representative because:
$(i)$ The mean is significantly influenced by extreme values (outliers) such as $11, 96,$ and $98$,which pull the average away from the central cluster of scores.
$(ii)$ The median provides a better measure of central tendency when the data set contains extreme values,as it represents the middle value of the ordered data set.
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