Question

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Answer 1

The line plot illustrates the capacity of the kitchen sink in gallons, and it has a sample size is 21. The distribution is positively skewed, with an appropriate measure of center is 16 and an appropriate measure of spread is 2.5

The description of the data

The dataset on the line plot represents the capacity of the kitchen sink.

The capacities are measured in gallons

The number of data values

This is the number of dots on the line plot.

There are 21 dots on the plot

Hence, the number of data values is 21

The shape of the distribution

The shape of the given distribution is positively skewed.

This is so because there are more points on the left of the distribution

Appropriate measure of center

The median is the appropriate measure of center for a skewed distribution.

So, we simply calculate the median.

The median position is calculated using

Median = 0.5 *  (n + 1) th

So, we have:

Median = 0.5 *  (21 + 1) th

Median = 11th

The 11th data element is 16

Hence, the value of an appropriate measure of center is 16

Appropriate measure of spread

The IQR is the appropriate measure of spread for a skewed distribution.

The IQR is:

IQR = Q3 – Q1

Where:

Q3 = 0.75(n + 1)th and  Q1 = 0.25(n + 1)th

This gives

Q3 = 0.75 * (21 + 1)th = 16.5

Q1 = 0.25(21 + 1)th = 5.5

The 16.5th element is 17.5, while the 5.5th element is 15

Recall that:

IQR = Q3 – Q1

So, we have:

IQR = 17.5 - 15

Evaluate

IQR = 2.5

Hence, the value of an appropriate measure of spread is 2.5

Read more about line plots at:

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