Question

Find the five-number summary and the interquartile range of the following data set. Determine if there are any outliers using the 1.5rule. 3-6. Prices of a new microwave at local stores: 67,54,46,56,52,54,52,91,66,61

Answer 1

The five-number summary of the data set is 46, 52, 54, 66, and 91. The interquartile range is 14. There are no outliers.

Step-by-step explanation:

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data in a set. To find the five-number summary, we first need to order the data set in ascending order:

46, 52, 52, 54, 54, 56, 61, 66, 67, 91

The five-number summary consists of the minimum (46), the first quartile (Q1 = 52), the median (Q2 = 54), the third quartile (Q3 = 66), and the maximum (91).

To calculate the IQR, we subtract Q1 from Q3: IQR = Q3 - Q1 = 66 - 52 = 14. So the interquartile range is 14.

To determine if there are any outliers, we can use the 1.5 rule. A value is considered an outlier if it is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR. In this case, we have no outliers since all values fall within the range of Q1 - 1.5 * IQR to Q3 + 1.5 * IQR.