Question

Nathan created a box plot based on this data set: 26 22 21 42 21 36 20 26 Nathan double-checked his original data and saw that he had swapped the digits of 24 and had written 42 instead. He updated his box plot using the correct value 24. How did this change his box plot? Select all that apply.

Answer 1

He created a box-plot with the data set {26, 22, 21, 42, 21, 36, 20, 26}.

If we sort the dataset we obtain: 20, 21, 21, 22, 26, 26, 36, 42.

This result in a median of 24, the average between 22 and 26.

Also, the maximum value is 42 while the minimum value is 20.

The quartiles are Q1 = 21 and Q3 = 31.

Now, we have the corrected dataset, with 24 instead of 42.

The sorted dataset is now: 20, 21, 21, 22, 24, 26, 26, 36.

The median is now the average between 22 and 24, so it is 23.

The minimum stays the same, but the maximum is now 36.

The firstquartile is still Q1 = 21 but the third quartile is now Q3 = 26.

Then, the maximum changed from 42 to 36, which is a decrease of 6 units.

The upper quartile, Q3, changed from 31 to 26, which is a decrease of 5 units.

The lower quartile, Q1, stay without changes.

The median also changed from 24 to 23.

The only true statement is: "the upper quartile decreased by 5".