Quartiles & IQR Quiz � Master Spread (6.SP.B.5)

1) Which is the best interpretation of an IQR of 6 cm for this data?

The average height is 6 cm

The middle half of plant heights are spread across 6 cm

Most plants are 6 cm tall

The tallest and shortest plants differ by 6 cm

The IQR measures the spread of the middle 50% of the data, so the best interpretation is that the middle half of plant heights are spread across 6 cm.

Explanation

The IQR measures the spread of the middle 50% of the data, so the best interpretation is that the middle half of plant heights are spread across 6 cm.

2) What is the median number of pages read?

33

36

40

35

To find the median, arrange the data in order: 12, 18, 25, 30, 30, 33, 37, 40, 42, 45, 47, 50. There are 12 data points, so the median is the average of the 6th and 7th values: (33 + 37) / 2 = 35.

Explanation

To find the median, arrange the data in order: 12, 18, 25, 30, 30, 33, 37, 40, 42, 45, 47, 50. There are 12 data points, so the median is the average of the 6th and 7th values: (33 + 37) / 2 = 35.

3) What is Q1 for this data set?

27.5

25

33

35

Q1 is the median of the lower half of the data. The lower half is: 12, 18, 25, 30, 30, 33. The median of this set is 27.5.

Explanation

Q1 is the median of the lower half of the data. The lower half is: 12, 18, 25, 30, 30, 33. The median of this set is 27.5.

4) What is Q3 for this data set?

42

45

43.5

47

Q3 is the median of the upper half of the data. The upper half is: 37, 40, 42, 45, 47, 50. The median of this set is 43.5.

Explanation

Q3 is the median of the upper half of the data. The upper half is: 37, 40, 42, 45, 47, 50. The median of this set is 43.5.

5) What is the IQR for this data set?

12

16

15

17

The IQR is the difference between Q3 and Q1: 43.5 - 27.5 = 16.

Explanation

The IQR is the difference between Q3 and Q1: 43.5 - 27.5 = 16.

6) Which statement best describes what the IQR represents for this class?

The difference between the lowest and highest pages read

The average number of pages read

The typical single value for pages read

The spread of the middle 50 percent of pages read

The IQR measures the spread of the middle 50% of the data.

Explanation

The IQR measures the spread of the middle 50% of the data.

7) What is the IQR of the data represented by the box plot?

15

12

21

33

The IQR is the distance between Q1 and Q3. From the box plot, calculate Q1 and Q3, then find the difference.

Explanation

The IQR is the distance between Q1 and Q3. From the box plot, calculate Q1 and Q3, then find the difference.

8) Which interval contains the middle 50 percent of the data?

8 to 20

20 to 41

14 to 29

8 to 41

The middle 50% of the data is represented by the IQR, which is between Q1 and Q3. From the box plot, find Q1 and Q3 to identify the correct interval.

Explanation

The middle 50% of the data is represented by the IQR, which is between Q1 and Q3. From the box plot, find Q1 and Q3 to identify the correct interval.

9) If a new data point of 60 is added, which measure is most affected?

Maximum

Q1

Median

IQR

Adding a high data point like 60 will affect the maximum and possibly the IQR but not Q1 or the median significantly.

Explanation

Adding a high data point like 60 will affect the maximum and possibly the IQR but not Q1 or the median significantly.

10) What is the median score?

75

81

78

83

The data set is: 55, 68, 72, 74, 75, 78, 81, 83, 85, 89, 92. The median is the middle value, which is 78.

Explanation

The data set is: 55, 68, 72, 74, 75, 78, 81, 83, 85, 89, 92. The median is the middle value, which is 78.

11) What are Q1 and Q3?

Q1 = 68, Q3 = 89

Q1 = 72, Q3 = 85

Q1 = 74, Q3 = 89

Q1 = 72, Q3 = 83

To find Q1 and Q3, divide the data into two halves: Q1 is the median of the lower half: 68. Q3 is the median of the upper half: 85.

Explanation

To find Q1 and Q3, divide the data into two halves: Q1 is the median of the lower half: 68. Q3 is the median of the upper half: 85.

12) What is the IQR?

11

17

20

13

The IQR is the difference between Q3 and Q1: 85 - 72 = 13.

Explanation

The IQR is the difference between Q3 and Q1: 85 - 72 = 13.

13) Which statement is true about the IQR?

It is calculated using the mean and standard deviation

It measures the spread of the middle half of the data

It always increases when you add more data points

It is the same as the range

The IQR measures the spread of the middle 50% of the data, not the entire data set.

Explanation

The IQR measures the spread of the middle 50% of the data, not the entire data set.

14) What is Q1?

12

10

14

15

The lower half of the data set is: 5, 7, 12, 12, 14, 15. The median of this set is 12.

Explanation

The lower half of the data set is: 5, 7, 12, 12, 14, 15. The median of this set is 12.

15) What is Q3?

18

20

24

21

The upper half of the data set is: 18, 18, 21, 21, 24, 30. The median of this set is 21.

Explanation

The upper half of the data set is: 18, 18, 21, 21, 24, 30. The median of this set is 21.

16) What is the IQR?

7

11

9

15

The IQR is the difference between Q3 and Q1: 21 - 12 = 9.

Explanation

The IQR is the difference between Q3 and Q1: 21 - 12 = 9.

17) Which class has the larger IQR?

Class A

Class B

They are the same

Not enough information

Class A’s IQR is (30 - 18 = 12), and Class B’s IQR is (36 - 12 = 24). Class B has the larger IQR.

Explanation

Class A’s IQR is (30 - 18 = 12), and Class B’s IQR is (36 - 12 = 24). Class B has the larger IQR.

18) What does the larger IQR tell you about that class?

Their middle 50 percent of data are more spread out

Their maximum is higher

Their data are more tightly clustered in the middle

Their mean is larger

A larger IQR means that the middle 50% of the data points are more spread out.

Explanation

A larger IQR means that the middle 50% of the data points are more spread out.

19) If both classes add the same high outlier, which statement is true?

The IQR for both classes will increase a lot

The IQR will decrease

The IQR equals the range

The IQR will likely stay the same for both classes

The IQR is not significantly affected by the addition of an outlier unless it changes Q1 or Q3. Since the outlier is high, it’s more likely to affect the range than the IQR.

Explanation

The IQR is not significantly affected by the addition of an outlier unless it changes Q1 or Q3. Since the outlier is high, it’s more likely to affect the range than the IQR.