Calculate & Interpret IQR Quiz (6.SP.B.5)

1) What is the median of this data set?

9

11

10

12

The middle value in the ordered list (11 numbers) is the 6th one. Counting to the 6th gives 10, so the median is 10.

Explanation

The middle value in the ordered list (11 numbers) is the 6th one. Counting to the 6th gives 10, so the median is 10.

2) What is the median temperature?

67

68

69

70

14 values. Median = average of 7th and 8th = (68 + 70)/2 = 69.

Explanation

14 values. Median = average of 7th and 8th = (68 + 70)/2 = 69.

3) What is Q1 for the temperature data?

62

63.5

64

63

Lower half: 58,60,62,63,65,67,68. Middle (4th) is 63. So Q1 = 63.

Explanation

Lower half: 58,60,62,63,65,67,68. Middle (4th) is 63. So Q1 = 63.

4) What is Q3 for the temperature data?

75

74.5

73

78

Upper half: 70,72,73,75,78,80,85. Middle (4th) is 75. So Q3 = 75.

Explanation

Upper half: 70,72,73,75,78,80,85. Middle (4th) is 75. So Q3 = 75.

5) What is the IQR for the temperature data?

9

12

11

10

IQR = Q3 − Q1 = 75 − 63 = 12.

Explanation

IQR = Q3 − Q1 = 75 − 63 = 12.

6) To identify potential outliers using the IQR method, you calculate boundaries at Q1 − 1.5(IQR) and Q3 + 1.5(IQR). If Q1 = 20 and Q3 = 40, what is the upper boundary for outliers?

40

50

65

70

IQR = 40 − 20 = 20. Upper boundary = Q3 + 1.5×IQR = 40 + 1.5×20 = 40 + 30 = 70.

Explanation

IQR = 40 − 20 = 20. Upper boundary = Q3 + 1.5×IQR = 40 + 1.5×20 = 40 + 30 = 70.

7) A data set has Q1 = 12, Q3 = 28, and IQR = 16. What is the lower boundary for identifying outliers?

−40

−12

0

4

Lower boundary = Q1 − 1.5×IQR = 12 − 1.5×16 = 12 − 24 = −12.

Explanation

Lower boundary = Q1 − 1.5×IQR = 12 − 1.5×16 = 12 − 24 = −12.

8) What is the first quartile (Q1) of this data set?

7

6

8

9

Lower half: 3, 5, 7, 8, 9. The middle of these is 7, so Q1 = 7.

Explanation

Lower half: 3, 5, 7, 8, 9. The middle of these is 7, so Q1 = 7.

9) Using the IQR method, what is the upper boundary for outliers?

47.5

45

41

35

Upper boundary = Q3 + 1.5×IQR = 28 + 1.5×13 = 28 + 19.5 = 47.5.

Explanation

Upper boundary = Q3 + 1.5×IQR = 28 + 1.5×13 = 28 + 19.5 = 47.5.

10) Is the score of 45 points an outlier?

No, because 45 is less than 47.5

Yes, because 45 is greater than 28

No, because 45 is the maximum value

Yes, because 45 is more than double Q1

45 < 47.5. So 45 is not an outlier.

Explanation

45 < 47.5. So 45 is not an outlier.

11) Two classes took the same math test. Class A has an IQR of 8 points, and Class B has an IQR of 22 points. What can you conclude?

Class A had higher test scores than Class B

Class B had more students than Class A

The median score was higher in Class B

Class A’s middle 50% of scores were more consistent than Class B’s

Smaller IQR means more consistent middle scores. Class A (IQR 8) is more consistent than Class B (IQR 22).

Explanation

Smaller IQR means more consistent middle scores. Class A (IQR 8) is more consistent than Class B (IQR 22).

12) What is the third quartile (Q3) of this data set?

12

13

14

15

Upper half: 12,14,15,16,22. Middle is 15. So Q3 = 15.

Explanation

Upper half: 12,14,15,16,22. Middle is 15. So Q3 = 15.

13) A data set showing monthly rainfall has Q1 = 2.5 inches, median = 3.8 inches, and Q3 = 5.1 inches. What is the IQR, and what does it represent?

IQR = 1.3 inches; the total range of rainfall

IQR = 2.6 inches; the spread of the middle 50% of rainfall amounts

IQR = 3.8 inches; the average monthly rainfall

IQR = 7.6 inches; the difference between the wettest and driest months

IQR = Q3 − Q1 = 5.1 − 2.5 = 2.6 inches. It shows the spread of the middle 50% of rainfall.

Explanation

IQR = Q3 − Q1 = 5.1 − 2.5 = 2.6 inches. It shows the spread of the middle 50% of rainfall.

14) What is the interquartile range (IQR) for this data set?

5

7

8

10

IQR = Q3 − Q1 = 15 − 7 = 8.

Explanation

IQR = Q3 − Q1 = 15 − 7 = 8.

15) What is Q1 for the ages of soccer participants?

7

7.5

8

9

Lower half (exclude median 9th): 6,7,7,8,8,9. Q1 = average of 3rd and 4th = (7 + 8)/2 = 7.5.

Explanation

Lower half (exclude median 9th): 6,7,7,8,8,9. Q1 = average of 3rd and 4th = (7 + 8)/2 = 7.5.

16) What is Q3 for the ages of soccer participants?

9

9.5

10

10.5

Upper half: 9,10,10,11,12,13. Q3 = average of 3rd and 4th = (10 + 11)/2 = 10.5.

Explanation

Upper half: 9,10,10,11,12,13. Q3 = average of 3rd and 4th = (10 + 11)/2 = 10.5.

17) What is the IQR for the ages of soccer participants?

3

2.5

4

5

IQR = Q3 − Q1 = 10.5 − 7.5 = 3.

Explanation

IQR = Q3 − Q1 = 10.5 − 7.5 = 3.

18) What does the IQR of 3 years tell us about the ages in this soccer league?

All players are exactly 3 years apart in age

The oldest player is 3 years older than the youngest

The middle 50% of players’ ages span 3 years

The average age is 3 years old

IQR of 3 means the middle 50% of ages span 3 years.

Explanation

IQR of 3 means the middle 50% of ages span 3 years.

19) A data set has Q1 = 15 and Q3 = 32. What is the IQR?

15

17

32

47

IQR = Q3 − Q1 = 32 − 15 = 17.

Explanation

IQR = Q3 − Q1 = 32 − 15 = 17.

20) The test scores for a class have Q1 = 68 and IQR = 18. What is Q3?

50

68

86

104

Q3 = Q1 + IQR = 68 + 18 = 86.

Explanation

Q3 = Q1 + IQR = 68 + 18 = 86.

Calculating and Interpreting IQR from Data Sets

1) What is the median of this data set?

2) What is the median temperature?

3) What is Q1 for the temperature data?

4) What is Q3 for the temperature data?

5) What is the IQR for the temperature data?

6) To identify potential outliers using the IQR method, you calculate boundaries at Q1 − 1.5(IQR) and Q3 + 1.5(IQR). If Q1 = 20 and Q3 = 40, what is the upper boundary for outliers?

7) A data set has Q1 = 12, Q3 = 28, and IQR = 16. What is the lower boundary for identifying outliers?

8) What is the first quartile (Q1) of this data set?

9) Using the IQR method, what is the upper boundary for outliers?

10) Is the score of 45 points an outlier?

11) Two classes took the same math test. Class A has an IQR of 8 points, and Class B has an IQR of 22 points. What can you conclude?

12) What is the third quartile (Q3) of this data set?

13) A data set showing monthly rainfall has Q1 = 2.5 inches, median = 3.8 inches, and Q3 = 5.1 inches. What is the IQR, and what does it represent?

14) What is the interquartile range (IQR) for this data set?

15) What is Q1 for the ages of soccer participants?

16) What is Q3 for the ages of soccer participants?

17) What is the IQR for the ages of soccer participants?

18) What does the IQR of 3 years tell us about the ages in this soccer league?

19) A data set has Q1 = 15 and Q3 = 32. What is the IQR?

20) The test scores for a class have Q1 = 68 and IQR = 18. What is Q3?