Understanding Quartiles and Ranges

What is the first quartile (Q1) of the data set: 3, 7, 8, 12, 14, 18, 20?

• 12

• 8

• 7

• 14

Calculate the third quartile (Q3) for the following data: 5, 10, 15, 20, 25, 30, 35, 40.

• 40

• 35

• 30

• 32.5

What is the median of the data set: 2, 4, 6, 8, 10, 12, 14?

• 6

• 10

• 8

• 12

Determine the interquartile range (IQR) for the data: 1, 3, 5, 7, 9, 11, 13, 15.

• 8

• 12

• 10

• 6

If Q1 is 25 and Q3 is 35, what is the interquartile range?

• 10

• 20

• 5

• 15

Explain the significance of the first quartile in a data set.

• The first quartile represents the median of the data set.

• The first quartile is the highest value in the data set.

• The first quartile is irrelevant to understanding data distribution.

• The first quartile is significant as it indicates the 25th percentile of a data set, helping to understand its distribution.

How do you find the median of an ungrouped data set?

• Count the total number of values in the data set.

• Calculate the average of the data set.

• Arrange the data in order and find the middle value(s).

• Select the largest value in the data set.

Given the data set: 4, 8, 12, 16, 20, what is the value of Q2?

• 12

• 20

• 16

• 8

What does the interquartile range tell you about a data set?

• The interquartile range measures the total number of data points.

• The interquartile range tells you the spread of the middle 50% of a data set.

• The interquartile range shows the average of the data set.

• The interquartile range indicates the maximum value in the data set.

If a data set has an IQR of 10, what can you infer about the spread of the middle 50% of the data?

• The middle 50% of the data has a spread of 10 units.

• The middle 50% of the data has a spread of 5 units.

• The middle 50% of the data is concentrated in a smaller range than 10 units.

• The IQR indicates the total range of the data set.