IXL - Choose appropriate measures of center and variation (Geometry practice)

At scout camp, Bill and his troop members each built a boat out of a sheet of foil. After all the scouts got their boats floating in the pool, each counted how many pennies could be added to his boat before it sank. This histogram shows their findings.

0-49

50-99

100-149

150-199

200-249

250-299

300-349

Pennies added

Number of boats

Foil boats

Complete the sentences.

The distribution of the number of pennies is best described as . So, the is a more appropriate measure of center than the .

ref_doc_title.

Learn with an example

question

Miguel has a booth at the Cards, Comics, and Games Convention, where he sells vintage trading cards. This histogram shows the distribution of the number of trading cards he's sold to each customer so far today.

1-3

4-6

7-9

10-12

13-15

16-18

Number of trading cards sold

Number of customers

Trading card sales

Complete the sentences.

The distribution of the numbers of trading cards sold is best described as . So, the is a more appropriate measure of variation than the .

key idea

Mean and median are measures of center.

The mean is calculated by taking the average of all the values in a data set.
The median is found by ordering the values in a data set from least to greatest, then selecting the middle value.

Standard deviation and interquartile range (IQR) are measures of variation.

The standard deviation measures how much data values typically vary from the mean.
The IQR is the range of the middle 50% of the data set.

The mean and standard deviation can be strongly affected by the shape of a distribution and by outliers. So, they are appropriate measures for symmetric distributions but may not be appropriate for skewed distributions or when there are outliers.

Since the median is the middle value in a data set, it is less affected by the shape of a distribution or by outliers. And, since the IQR is the range of the middle 50% of the data set, it is also less affected by the shape or by outliers. So, they are almost always appropriate measures.

solution

Most of the data values are on the left, and the "tail" of the graph extends to the right. So, the distribution is skewed to the right. It does not have a symmetric shape.

1-3

4-6

7-9

10-12

13-15

16-18

Number of trading cards sold

Number of customers

Trading card sales

These sentences are correct.

The distribution of the numbers of trading cards sold is best described as not

symmetric.

So, the interquartile range is a more appropriate measure of variation than the standard

deviation.

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	03

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

JJ.11Describe distributions in line plots

Variance and standard deviation

HH.4Interpret histograms

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!