The correct answer is option B. Damaria’s median sale is $52.
What is mean of some observations ?
Mean of some observations is actually the average of those observations.
- Mean can be obtained by adding all the observations and then dividing the sum by total number of observations.
Mean = [tex]\frac{sum}{total}[/tex]
What is median ?
The median is the middle value in a list if all the observations are ordered in ascending order.
- If the set of observations is even, then the median is the (n/2)th observation+(n/2 +1)th observation ) / 2
What is mode?
The mode is the most frequently occurring value in the list.
What is range ?
Range is the difference between the highest and the lowest observation in the list.
How to find which center should be used to best represent the given data?
The observations are $52, $60, $48, $52, $46, $52, $28, $192, $71, $59.
∴ Mean = $ [tex](\frac{52+60+48+52+46+52+28+192+71+59}{10})[/tex] = $66
Clearly, the mean doesnot matches with the answer.
So, option A is incorrect.
- Now arranging the data in ascending order,
$28 , $46 , $48 ,$52 ,$52 ,$52 ,$59 ,$60 , $71 ,$192
Here the set of observations is even
∴ Median = $(52 + 52 )/2 =$52
Clearly option B matches and it is correct.
- In the given set of data $52 occurs thrice and no other observations occurs thrice or more. So, $52 is the mode.
Clearly option C matches and it is correct.
- In the given set of data, the highest data is $192 and the lowest data is $28.
Range = $(192 - 28) = $164
Option D is also correct.
- Here, though options B ,C, D are correct , Median is used to represent the data at its best because The median is less affected by outliers and skewed data.
So, the center should be used to best represent the data is median.
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