IXL | Compare populations using measures of center and spread

Ross works for the Great Waves water-sport rental company. He recorded the rental times for a sample of 7 kayak rentals and 7 speed boat rentals. The results are recorded in the line plots.

Kayak

Rental times (hours)

Boat

Rental times (hours)

Complete the table. Write your answers as whole numbers or decimals rounded to the nearest tenth.

	Median	Interquartile range
Kayak
Boat	3	2

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Learn with an example

question

The Rapid Refreshments company placed two vending machines at the Fortune Valley shopping mall: one with drinks and one with snacks. The company manager tracked the amount of money made from each vending machine for the first 8 months. The table shows the results.

Month	Drinks	Snacks
March	$750	$850
April	$800	$800
May	$900	$650
June	$1,000	$600
July	$ 1,000	$750
August	$950	$900
September	$950	$950
October	$850	$900

Complete the table. Write your answers as whole numbers or decimals rounded to the nearest tenth.

	Mean	Mean absolute deviation
Drinks	$900	$
Snacks	$	$100

key idea

The mean is the average value of the data set. It describes the center of the data set.

The mean absolute deviation (MAD) is the average distance between the data values and the mean. It describes the variability of the data set.

solution

First, find the mean absolute deviation of the money made from the vending machine with drinks for the 8-month sample. Start by finding the distance from the mean for each value. That is the same as the absolute value of the difference between the value and the mean.

750

–

900

150

800

–

900

100

900

–

900

1,000

–

900

100

1,000

–

900

100

950

–

900

950

–

900

850

–

900

Now add all of these differences and divide by the total number of data values in the sample.

150

100

The mean absolute deviation of the money made from the vending machine with drinks for the 8-month sample is

$75.

Next, find the mean amount of money made for the vending machine with snacks for the 8-month sample. Add all of the amounts and then divide by the total number of months in the sample.

850

800

650

600

750

900

950

900

800

The mean for the vending machine with snacks for the 8-month sample is

$800.

Finally, use these values to complete the table.

	Mean	Mean absolute deviation
Drinks	$900	$75
Snacks	$800	$100

Looking for more? Try this:

$Confetti$

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Teacher tools

Work it out

Not feeling ready yet? These can help:

HH.5Calculate mean absolute deviation

HH.6Calculate quartiles and interquartile range

GG.13Box plots

HH.2Interpret charts and graphs to find mean, median, mode, and range

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