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All Common Core: High School - Statistics and Probability Resources

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Flashcards: Use Statistics to Compare Center and Spread of Data Distribution: CCSS.Math.Content.HSS-ID.A.2

$Set\ A=\left \{ 5,5,5,5,5 \right \}$

$Set\ B=\left \{ 0,5,10,15,20 \right \}$

Which statement about the two sets is TRUE?

The standard deviation of Set B is twice the standard deviation of Set A.

Of the two sets, Set A has the smaller mean, median, and standard deviation.

In Set B, the mean is larger than the median.

Of the two sets, Set B has the smaller mean, median, and standard deviation.

Set A has a smaller standard deviation but larger range than Set B.

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Flashcards: Use Statistics to Compare Center and Spread of Data Distribution: CCSS.Math.Content.HSS-ID.A.2

$Set\ A=\left \{ 5,5,5,5,5 \right \}$

$Set\ B=\left \{ 0,5,10,15,20 \right \}$

Which statement about the two sets is TRUE?

Your answer:

The standard deviation of Set B is twice the standard deviation of Set A.

Your answer:

In Set B, the mean is larger than the median.

Your answer:

Of the two sets, Set B has the smaller mean, median, and standard deviation.

Your answer:

Set A has a smaller standard deviation but larger range than Set B.

Correct answer:

Of the two sets, Set A has the smaller mean, median, and standard deviation.

Explanation:

Flashcards: Use Statistics to Compare Center and Spread of Data Distribution: CCSS.Math.Content.HSS-ID.A.2

A plumber salvages old brass fittings in order to make extra money by selling scrap metal. He tallies his scrap totals for a five month period. The plumber collected the following pounds of brass in a five month period:

Screen shot 2015 11 25 at 11.15.38 am

Find the proper measure of center and spread for this data set.

$\textup{Mean}=36.2, \ \textup{MAD}=7.96$

$\textup{Mean}=32.6, \ \textup{MAD}=9.76$

$\textup{Mean}=27, \ \textup{MAD}=9.67$

$\textup{Mean}=28.5, \ \textup{MAD}=8.67$

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Flashcards: Use Statistics to Compare Center and Spread of Data Distribution: CCSS.Math.Content.HSS-ID.A.2

Screen shot 2015 11 25 at 11.15.38 am

Find the proper measure of center and spread for this data set.

Your answer:

$\textup{Mean}=36.2, \ \textup{MAD}=7.96$

Your answer:

$\textup{Mean}=27, \ \textup{MAD}=9.67$

Your answer:

$\textup{Mean}=28.5, \ \textup{MAD}=8.67$

Correct answer:

$\textup{Mean}=32.6, \ \textup{MAD}=9.76$

Explanation:

There are several common measures of center and spread for a given data set. The most common measures of center are the mean and median. The mean represents the arithmetic average of a set and the median is the middlemost value. On the other hand the most common measures of spread are the mean absolute deviation (MAD) and inter-quartile range (IQR).

The measures of center and spread vary for different sets of data. The mean and MAD are used together to analyze data presented in bar charts or histograms while the median and IQR are most commonly used for box and whisker plots.

Lets look at our data. We have the following pounds of brass for the five-month period starting in January:

$25,\ 26, \ 27, \ 28, \ 57$

First let's plot this data on a bar graph.

Brass

Now, let's use the mean and MAD to calculate the center and spread of the data respectively.

The center should be calculated using the mean. The mean is the arithmetic average and is found by adding all of the values together and dividing by the number of values in the series.

$\textup{Mean}=\frac{\sum x}{n}$

$\textup{Mean}=\frac{25+26+27+28+57}{5}$

$\textup{Mean}=\frac{163}{5}$

$\textup{Mean}=32.6$

Now, let's find the spread of the data using the MAD. The MAD describes how data varies about the mean. The MAD is calculated by finding out how much each data points deviates from the mean and dividing by the total number of values in the series.

$\textup{MAD}=\frac{\sum \left | x-\textup{mean}\right |}{n}$

First, let's find out how much each value varies from the mean by taking the absolute value of the mean minus each individual value.

$\left | 25-32.6\right |=7.6$

$\left | 26-32.6\right |=6.6$

$\left | 27-32.6\right |=5.6$

$\left | 28-32.6\right |=4.6$

$\left | 57-32.6\right |=24.4$

Now, we need to add up these values and divide that total by the number of values in the series.

$\textup{MAD}=\frac{7.6+6.6+5.6+4.6+24.4}{5}$

$\textup{MAD}=\frac{48.8}{5}$

$\textup{MAD}=9.76$

The MAD is the value that each individual number in the set deviates from the mean; therefore, it represents the spread of the series.

The correct answer for this problem is the following:

$\textup{Mean}=32.6, \ \textup{MAD}=9.76$

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All Common Core: High School - Statistics and Probability Resources

Flashcards: Use Statistics to Compare Center and Spread of Data Distribution: CCSS.Math.Content.HSS-ID.A.2

Flashcards: Use Statistics to Compare Center and Spread of Data Distribution: CCSS.Math.Content.HSS-ID.A.2

Flashcards: Use Statistics to Compare Center and Spread of Data Distribution: CCSS.Math.Content.HSS-ID.A.2

Flashcards: Use Statistics to Compare Center and Spread of Data Distribution: CCSS.Math.Content.HSS-ID.A.2

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