Answer:
range: 20
median: 38
Lower quartile and upper quartile: 29 and 42.5
Interquartile range: 13.5
Which value was affected the most: range
The value of the range was mostly affected after the outlier crossed out.
This is determined by calculating all the values before and after the outlier 72.
The range of data is calculated by taking the difference between the highest value and the lowest value of the data set.
Range=maximum value - minimum value
Given a table of data points as 35, 45, 26, 32, 46, 38, 39, 40, 26, 72.
Finding the values given in the list before crossing out the outlier 72:
Range: 72-26=46
Median: 38.5
Arranging in the ascending order
26, 26, 32, 35, 38, 39, 40, 45, 46, 72
Then, median=[tex]\frac{38+39}{2}[/tex]=38.5
Lower quartile: Q1=32
Upper quartile: Q3=45
IQR: Q3-Q1=45-32=13
Finding the values given in the list after crossing out the outlier 72:
The data set now has 9 elements with data points as 35, 45, 26, 32, 46, 38, 39, 40, 26
Range: 46-26=20
Median: 38
Arranging in the ascending order
26, 26, 32, 35, 38, 39, 40, 45, 46
Since odd number of data points, the median is at the middle point which is 38
Lower quartile: Q1=29
[tex]Q_1=\frac{1}{4} (n+1)[/tex] th term (n=9)
Q1=10/4=2.5
So, the median is between 26 and 32 which is 29
Upper quartile: Q3=42.5
[tex]Q_3=\frac{3}{4} (n+1)[/tex] th term (n=9)
Q3=7.5
So, the median is between 40 and 45 which is 42.5
IQR: Q3-Q1=42,5-29=13.5
From these results, it is observed that only the range is affected mostly when outlier 72 is removed.
Learn more about the range here:
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