Apply IQR in Real Contexts Quiz (HSS.ID.A.2)

1) Which statement best describes reliability of typical scores using IQR?

Section 1 is slightly more consistent in the middle range

Section 2 is more consistent in the middle range

Both are equally consistent

IQR cannot compare consistency

Section 1 has a smaller IQR and is more consistent.

Explanation

Section 1 has a smaller IQR and is more consistent.

2) If the distributions are right-skewed, why is comparing medians and IQRs more appropriate than means and standard deviations?

Medians and IQRs are resistant to extreme values and skew

IQR is more resistant to extreme values, making it a better measure for skewed distributions.

Explanation

IQR is more resistant to extreme values, making it a better measure for skewed distributions.

3) The company wants to predict next-day watch time for typical users using the middle 50%. Which group’s prediction would likely have a tighter range?

Casual

Avid

Both equal

Need mean and standard deviation

Casual group has a tighter IQR and more predictable mid-range watch times.

Explanation

Casual group has a tighter IQR and more predictable mid-range watch times.

4) If a user in Casual logs 5.0 hours one day, which is most accurate?

It is likely an outlier since it is far above Q3 relative to IQR

It is not an outlier because 5.0 < Q3 + IQR

It must be an error

The value is likely an outlier because it exceeds Q3 + IQR.

Explanation

The value is likely an outlier because it exceeds Q3 + IQR.

5) Which group has more variability among typical users?

Avid

Casual

Avid

Casual

Avid group has more variability, as it has a larger IQR.

Explanation

Avid group has more variability, as it has a larger IQR.

6) What are the IQRs?

Casual IQR = 1.3; Avid IQR = 1.9

Casual IQR = 1.0; Avid IQR = 2.0

Casual IQR = 1.2; Avid IQR = 2.0

Casual IQR = 0.8; Avid IQR = 2.5

IQRs for Casual and Avid groups are provided.

Explanation

IQRs for Casual and Avid groups are provided.

7) Using the 1.5×IQR rule for low outliers, which city is more likely to flag extremely low incomes?

City X, because a larger IQR lowers the low-outlier cutoff less than Q1 alone matters

City Y, because it has a higher Q1

City X, because it has a lower median

City Y, because it has a lower IQR setting a higher low-outlier cutoff

City X’s larger IQR means it will flag low incomes more easily.

Explanation

City X’s larger IQR means it will flag low incomes more easily.

8) A policy analyst wants the city with more predictable mid-range incomes. Which city should they select based on IQR?

City Y

City X

Both cities

City X

City Y has a smaller IQR, meaning more predictable mid-range incomes.

Explanation

City Y has a smaller IQR, meaning more predictable mid-range incomes.

9) Which city shows greater income disparity within the middle 50%?

City X

City Y

City X

City Y

City X has a larger IQR, meaning it has more income disparity in the middle 50%.

Explanation

City X has a larger IQR, meaning it has more income disparity in the middle 50%.

10) Compute IQRs for City X and City Y.

City X IQR = 35; City Y IQR = 22

City X IQR = 20; City Y IQR = 18

City X IQR = 25; City Y IQR = 20

City X IQR = 15; City Y IQR = 12

IQR calculations for both City X and City Y are provided.

Explanation

IQR calculations for both City X and City Y are provided.

11) What is the IQR for Route A?

7

15

16

25

IQR is the difference between Q3 and Q1.

Explanation

IQR is the difference between Q3 and Q1.

12) If a score of 98 appears in Section 2, is it necessarily an outlier by the 1.5×IQR rule?

No, because the outlier cutoff is Q3 + 1.5×IQR

Yes, because it is more than 10 points above Q3

No, because medians determine outliers

Yes, because it’s above Q3

Since 98 is below the outlier threshold of Q3 + 1.5×IQR, it is not an outlier.

Explanation

Since 98 is below the outlier threshold of Q3 + 1.5×IQR, it is not an outlier.

13) For identifying potential outliers using 1.5×IQR above Q3, which section sets a higher outlier threshold?

Section 2, because it has a larger IQR and higher Q3

Both have the same threshold

Section 2 has both a larger IQR and higher Q3, setting a higher threshold for outliers.

Explanation

Section 2 has both a larger IQR and higher Q3, setting a higher threshold for outliers.

14) Which section has more variability in student performance?

Section 2

Section 1

Both are equal

Cannot determine

Section 2 has a larger IQR and shows more variability.

Explanation

Section 2 has a larger IQR and shows more variability.

15) Compute IQRs for both sections. Which is correct?

Section 1 IQR = 16; Section 2 IQR = 20

Section 1 IQR = 10; Section 2 IQR = 12

Section 1 IQR = 18; Section 2 IQR = 20

Section 1 IQR = 14; Section 2 IQR = 22

These are the correct IQR calculations for Section 1 and Section 2.

Explanation

These are the correct IQR calculations for Section 1 and Section 2.

16) If both routes have similar medians, what does the difference in IQR suggest?

Route A has more variability despite similar central tendency

The distributions must be symmetric

Route B has more variability and higher center

IQR shows variability, and a higher IQR indicates more variability.

Explanation

IQR shows variability, and a higher IQR indicates more variability.

17) For consistent commuter planning, which route is preferable based on IQR alone?

Route B

Route A

Both are equally consistent

Cannot determine without means

Route B has a smaller IQR and is more consistent in travel times.

Explanation

Route B has a smaller IQR and is more consistent in travel times.

18) If a 60-minute trip occurs on Route A, which statement is most justified using the IQR?

It is likely an outlier because it is far above Q3

It proves Route A is slower than Route B

It is definitely a typical value

It must be within the middle 50%

Since it’s far above Q3, it’s likely an outlier.

Explanation

Since it’s far above Q3, it’s likely an outlier.

19) Which route shows greater variability in middle 50% of travel times?

Route A, because its IQR is larger

Route B, because its Q1 is higher

Route A, because its Q3 is lower

Route A, because its median is higher

The route with the larger IQR shows greater variability in travel times.

Explanation

The route with the larger IQR shows greater variability in travel times.

20) What is the IQR for Route B?

11

5

22

33

IQR is the difference between Q3 and Q1.

Explanation

IQR is the difference between Q3 and Q1.

Applying IQR to Real-World Problems

1) Which statement best describes reliability of typical scores using IQR?

2)

What first name or nickname would you like us to use?

2) If the distributions are right-skewed, why is comparing medians and IQRs more appropriate than means and standard deviations?

3) The company wants to predict next-day watch time for typical users using the middle 50%. Which group’s prediction would likely have a tighter range?

4) If a user in Casual logs 5.0 hours one day, which is most accurate?

5) Which group has more variability among typical users?

6) What are the IQRs?

7) Using the 1.5×IQR rule for low outliers, which city is more likely to flag extremely low incomes?

8) A policy analyst wants the city with more predictable mid-range incomes. Which city should they select based on IQR?

9) Which city shows greater income disparity within the middle 50%?

10) Compute IQRs for City X and City Y.

11) What is the IQR for Route A?

12) If a score of 98 appears in Section 2, is it necessarily an outlier by the 1.5×IQR rule?

13) For identifying potential outliers using 1.5×IQR above Q3, which section sets a higher outlier threshold?

14) Which section has more variability in student performance?

15) Compute IQRs for both sections. Which is correct?

16) If both routes have similar medians, what does the difference in IQR suggest?

17) For consistent commuter planning, which route is preferable based on IQR alone?

18) If a 60-minute trip occurs on Route A, which statement is most justified using the IQR?

19) Which route shows greater variability in middle 50% of travel times?

20) What is the IQR for Route B?