Outliers Warmup 3

When using IQR to find outliers, which formula will identify the upper limit?

• Q3 - 1.5(IQR)

• Q1 + 1.5(IQR)

• Q1 - 1.5(IQR)

• Q3 + 1.5(IQR)

Answer explanation

To identify the upper limit for outliers using IQR, the correct formula is Q3 + 1.5(IQR). This formula adds 1.5 times the interquartile range to the third quartile (Q3) to determine the threshold for upper outliers.

When using IQR to find outliers, which formula will identify the lower limit?

• Q3 - 1.5(IQR)

• Q1 + 1.5(IQR)

• Q1 - 1.5(IQR)

• Q3 + 1.5(IQR)

Answer explanation

To identify the lower limit for outliers using IQR, the correct formula is Q1 - 1.5(IQR). This calculation helps determine values that fall below this threshold, indicating potential outliers.

Which of the following best describes the process of finding the interquartile range for a set of data?

• Add the biggest and smallest numbers.

• Place the numbers in order from least to greatest and find the middle.

• Find the difference between the maximum and the minimum.

• Subtract Q1 from Q3.

Answer explanation

The interquartile range (IQR) is found by subtracting the first quartile (Q1) from the third quartile (Q3). This measures the spread of the middle 50% of the data, making 'Subtract Q1 from Q3' the correct choice.

Using the information below, identify which of the following is an outlier:
Q1 = 3
Q2 = 7
Q3 = 12

• 22

• 25.5

• -8.5

• 26

Answer explanation

To identify outliers, calculate the interquartile range (IQR): IQR = Q3 - Q1 = 12 - 3 = 9. Outliers are values < Q1 - 1.5*IQR or > Q3 + 1.5*IQR. Here, 26 is > 12 + 1.5*9 = 25.5, making it an outlier.

Find the Median of the following numbers:
84, 88, 72, 74, 98, 16, 94 

• 16

• 98

• 84

• There is no median.

Answer explanation

To find the median, first sort the numbers: 16, 72, 74, 84, 88, 94, 98. The median is the middle value, which is 84 in this case, as it is the fourth number in the sorted list.

Use the 1.5 IQR rule to determine if there are any outliers for the following numbers:
84, 88, 72, 74, 98, 16, 94 

• Yes, 16 is an outlier.

• Yes, 33 is an outlier.

• Yes, 98 is an outlier.

• There are no numbers less than 39 or greater than 124, therefore there are no outliers.

Answer explanation

To find outliers using the 1.5 IQR rule, calculate Q1 (72), Q3 (94), and IQR (22). The lower bound is 39 and the upper bound is 124. Since 16 is below 39, it is an outlier.