Question

people at a library were asked how many states they had visited. below is a stemplot of all of the data except for one value. number of states visited 0|8 9 9 9 1|0 1 2 2 2 4 5 6 6 8 8 2|1 2 7 7 7 3|1 key: 2|7 = 27 states which of the following statements is true? if the missing data value were 32, the iqr would change substantially. if the missing data value were 32, the range would change substantially. if the missing data value were 50, the iqr of the data would change substantially. if the missing data value were 50, the range of the data would change substantially.

Explanation:

Step1: Find current range

The current minimum value from the stemplot is 8 and the maximum is 31. The current range is $31 - 8=23$.

Step2: Analyze effect of 32 as missing value

If the missing value is 32, the new maximum is 32. The new range is $32 - 8 = 24$. The change in range is $24-23 = 1$, which is not substantial.

Step3: Analyze effect of 50 as missing value

If the missing value is 50, the new maximum is 50. The new range is $50 - 8=42$. The change in range is $42 - 23=19$, which is substantial.

Step4: Recall IQR concept

The inter - quartile range (IQR) is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). Adding a single value (either 32 or 50) will not change the position of $Q_1$ and $Q_3$ substantially for a data - set of this size.

Answer:

If the missing data value were 50, the range of the data would change substantially.