Question

A company selling clothing on the Internet reports that the packages it ships have a median weight of 4343 ounces and an IQR of 2424 ounces.

​a) The company plans to include a sales flyer weighing 55 ounces in each package. What will the new median and IQR​ be?

​b) If the company recorded the shipping weights of the packages with the sales flyers included in pounds instead of​ ounces, what would the median and IQR​ be?

​a) The new median will be ___ ounces.The new IQR will be ___ ounces.

Answer 1

Solution: Given that median = 43, IQr = 24

a) The weight in each package increases by 5 ounces.

The median is the midddle value of the sorted data set and thus the median will change in the same way that all data values change:

Median = 43+5 = 48

the interquartile range IQR measures that spread of the data values.Since the data values all increase by the same value,the spread of the data values remains unaffected and thus the IQR remains the same.

IQR = 24

b) 1lb = 16 oz.

The new median in pounds is the median in ounces divided by 16

Median = 48/16 = 3

The new IQR in pounds is the IQR in qunces divided by 16

IQR = 24/16 = 1.5