Standard Deviation Practice Variability

Which box plot has a greater measure of variability?

• 
• 
• Both have the same variability.

The depth of two lakes is measured at multiple spots. For the first lake, the mean depth is about 45 feet with a standard deviation of 8 feet. For the second lake, the mean depth is about 60 feet with a standard deviation of 27 feet. Noah says the second lake is generally deeper than the first lake. Do you agree with Noah?

The dot plots display the height, rounded to the nearest foot, of maple trees from two different tree farms. Compare the mean and standard deviation of the two data sets.

What does the standard deviation tell you about the trees at these farms?

The data set and some summary statistics are listed. 11.5, 12.3, 13.5, 15.6, 16.7, 17.2, 18.4, 19, 19.5, 21.5 mean: 16.52 median: 16.95 standard deviation: 3.11 IQR: 5.5 How does adding 5 to each of the values in the data set impact the shape of the distribution?

• The shape becomes skewed to the right.

• The shape remains symmetric.

• The shape becomes skewed to the left.

Select all the statements that are true about standard deviation.

• It is a measure of center.

• It is a measure of variability.

• It is the same as the MAD.

• It is calculated using the mean.

• It is calculated using the median.

Three drivers competed in the same fifteen drag races. The mean and standard deviation for the race times of each of the drivers are given. Driver A had a mean race time of 4.01 seconds and a standard deviation of 0.05 seconds. Driver B had a mean race time of 3.96 seconds and a standard deviation of 0.12 seconds. Driver C had a mean race time of 3.99 seconds and a standard deviation of 0.19 seconds. Which driver had the fastest typical race time?

• Driver A

• Driver B

• Driver C

The widths, in millimeters, of fabric produced at a ribbon factory are collected. The mean is approximately 23 millimeters and the standard deviation is approximately 0.06 millimeters. Interpret the mean and standard deviation in the context of the problem.

What is the standard deviation?

A set of data has ten numbers. The mean of the data is 12 and the standard deviation is 0. What values could make up a data set with these statistics?