Question

lesson 2.1 – describing location in a distribution exit ticket
lesson app 2.1 a house divided!
the u.s. house of representatives has 435 voting members. each state is allocated a number of
seats in the house based on its population when the census is taken every 10 years. a dotplot of the
number of representatives from each of the 50 states in 2019 is shown, along with summary
statistics. the red point on the graph is for the state of ohio, with its 16 representatives.

n	mean	sd	min	q₁	med	q₃	max

1. find the percentile for ohio. interpret this value.

1. south carolina is at the 52nd percentile of the distribution. how many representatives did

south carolina have in 2019?

1. calculate and interpret the standardized score for ohio.

how many counties does each state have? the table displays summary statistics for these data.

n	mean	sd	min	q₁	med	q₃	max

1. ohio has 88 counties. in which distribution— number of representatives or number of

counties— is ohio farther from the mean? justify your answer.

Explanation:

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Step1: Count states with reps <16

There are 50 total states. From the dotplot, only the points at 20,30,35,40,53 are above 16, so $50-5=45$ states have fewer representatives than Ohio.

Step2: Compute percentile

$\text{Percentile} = \frac{\text{Number of values less than }16}{n} \times100 = \frac{45}{50} \times100 = 90$
Interpretation: 90% of states have fewer than 16 representatives.
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Step3: Locate 52nd percentile

The 52nd percentile means 52% of 50 = 26 states have fewer representatives. $Q_2=\text{Med}=10$, and $Q_3=13$. 26 states fall at or below 10, so the 52nd percentile is 10.
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Step4: Calculate z-score for Ohio reps

Standardized score formula: $z=\frac{x-\mu}{\sigma}$
$z=\frac{16-8.7}{9.723} = \frac{7.3}{9.723} \approx 0.75$
Interpretation: Ohio's representatives are 0.75 standard deviations above the mean.
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Step5: Compute z-score for Ohio counties

$z_{\text{counties}}=\frac{88-62.82}{46.421}=\frac{25.18}{46.421}\approx0.54$
Compare to $z_{\text{reps}}\approx0.75$. Since $0.75>0.54$, Ohio is farther from the mean in the representatives distribution.
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Answer:

1. 90th percentile: 90% of U.S. states have fewer than 16 House representatives.
2. 10
3. $\approx0.75$: Ohio's representative count is 0.75 standard deviations above the national mean.
4. Ohio is farther from the mean in the number of representatives distribution, as its standardized score ($\approx0.75$) is larger than its standardized county score ($\approx0.54$).