Chapter 6, Problem 1E

a)

To determine

To find new median and IQR.

Answer to Problem 1E

Median = 72 ounces and IQR = 40 ounces.

Explanation of Solution

Given:

Median = 68 ounces

IQR = 40 ounces

First, we need to understand about median and IQR.

Median: Median is the middle of the sorted data

IQR: Interquartile range measures the spread of the data.

Therefore, the weight in each package increased by 4 ounces. So, median will change in the same way that all data values change.

Hence, median = 68+4 = 72 ounces.

It is known that, the data values all increase by the same value, the spread of the data values remains unaffected. Therefore, in this case, the IQR remains unchanged.

Hence, IQR = 40 ounces.

b)

To determine

To convert median and IQR into pounds instead of ounces.

Answer to Problem 1E

Median = 4.5 pounds and IQR = 2.5 pounds.

Explanation of Solution

Given:

Median = 72 ounces

IQR = 40 ounces

1 lb = 16 oz.

Calculation:

First, we need to understand about median and IQR.

Median: Median is the middle of the sorted data

IQR: Interquartile range measures the spread of the data.

Therefore,

  $Median=\frac{72}{16}=4.5pounds$

And

  $\text{IQR }=\frac{40}{16}=2.5pounds$