The median of given data is 42.5
And
The median after replacing 42 with 92 is 44.5
Step-by-step explanation:
A median is the middle value of the data that divided the data in two equal parts
Given data is:
46 43 39 48 52 40 42 98 20 38
First of all, the data has to arranged in ascending order
20, 38, 39, 40, 42, 43, 46, 48, 52, 98
As the number of values is even, n=10, the median will be the average of middle two numbers
20, 38, 39, 40, 42, 43, 46, 48, 52, 98
[tex]Median = \frac{42+43}{2}\\=\frac{85}{2}\\=42.5[/tex]
The median is 42.5
Now,
Replacing 42 with 92
20, 38, 39, 40, 92, 43, 46, 48, 52, 98
The data has to be re-arranged
So,
20, 38, 39, 40, 43, 46, 48, 52, 92, 98
As the number of values is same,
[tex]New\ median = \frac{43+46}{2}\\=\frac{89}{2}\\= 44.5[/tex]
Hence,
The median of given data is 42.5
And
The median after replacing 42 with 92 is 44.5
Keywords: Median, mode
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