Understanding Measures of Spread

What is the range of a data set?

• The average of all values

• The sum of all values

• The difference between the highest and lowest values

• The spread of the middle 50%.

What is the formula for calculating the interquartile range (IQR)?

• Q3 - Q1

• Q1 + Q3

• Maximum - Minimum

• Mean - Median

Why is the range important in analyzing data?

• It shows the consistency of the data points

• It highlights the variation between the highest and lowest values

• It eliminates outliers from the data set

• It calculates the mean

What does a small standard deviation indicate?

• Data values are far from the mean

• Data values are close to the mean

• Data set has outliers

• Data set has a large range

If Q1 = 10 and Q3 = 25, what is the IQR?

• 10

• 15

• 20

• 25

Which measure is most affected by outliers?

• Median

• Mean

• Range

• Interquartile Range (IQR)

Two cross country runners have the same average time for 5K races. What does a higher standard deviation indicate?

• The runner's times are more consistent

• The runner's times are more spread out

• The runner finishes the race faster overall

• The runner's times are identical in every race.

What does the interquartile range focus on?

• All data points

• The largest and smallest values

• The mean of the data set

• The middle 50% of data

Which transformation increases the standard deviation of a data set?

• Adding a constant to all values

• Reducing values close to the mean

• Keeping values unchanged

• Increasing values farther from the mean

What is the formula for calculating the range of a data set?

• Q3 - Q1

• Mean - Median

• Maximum - Minimum

• Q1 + Q3