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Q 11.

Expert-verifiedFound in: Page 105

Book edition
6th

Author(s)
Daren Starnes, Josh Tabor

Pages
837 pages

ISBN
9781319113339

Foreign-born residents The cumulative relative frequency graph shows the distribution of the percent of foreign-born residents in the $50$ states.

a. Estimate the interquartile range (IQR) of this distribution. Show your method.

b. What is the percentile for Arizona, which had $15.1\%$ foreign-born residents that year?

c. Explain why the graph is fairly flat between $20\%$ and $27.5\%$

d. Draw the histogram that corresponds to this graph.

Part (a) The value is $9.00$

Part (b) The percentile is $84$

Part (c) The cumulative relative frequency for these values is growing between $20\%$ and $27.5$ percent.

Part (d) The histogram is

The plot is:

The percentile of an individual is the percentage of the distribution that is less than the data value of the individual.

The third quartile and first quartile, according to the plot, are $12.75$ and $3.75$ respectively.

Thus, the interquartile range is:

$IQR={Q}_{3}-{Q}_{1}\phantom{\rule{0ex}{0ex}}=12.75-3.75\phantom{\rule{0ex}{0ex}}=9.00$

Thus, the required value is $9.00$

Create a vertical line that cuts the $x-$axis at $15.1$ to calculate the required percentage. Create a horizontal line to connect the vertical and horizontal lines. Both lines overlap at the $84th$ percentile, as can be seen.

Thus, the required percentile is $84$

Because of the minor rise in frequency for these values, the cumulative relative frequency for these values is growing between $20\%$ and $27.5$ percent.

The histogram could be constructed as:

Big sharks Here are the lengths (in feet) of 44 great white sharks:

A dot plot of the data and summary statistics are shown below. Is this distribution of shark length approximately Normal? Justify your answer based on the graph and the 68–95–99.7 rule.

n | Mean | SD | Min | Q1 | Med | Q3 | Max |

44 | 15586 | 2.55 | 9.4 | 13.55 | 15.75 | 17.2 | 22.8 |

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