Summary Statistics: Measures of Variation

Make up two data sets with 5 numbers each that have:

1. The same mean but different standard deviations.

2. The same standard deviation but different means.

Make up two data sets with 7 numbers that each have:

1. The same IQR but different medians.

2. Different IQRs but the same medians.

Suppose you buy a new car whose advertised gas mileage is 25 mpg (miles per gallon). After driving the car for several months, you find that you are getting only 21.4 mpg. You phone the manufacturer and learn that the standard deviation of gas mileage for cars of that model is 1.15 mpg.

1. Find the Z-score for the gas mileage of your car.

2. Does it appear that your car is getting unusually low gas mileag…

According to a local marathon club, the mean finishing time for a marathon is 274 minutes, with a standard deviation of 63 minutes.

1. If I can run a marathon with a finishing time of 170 minutes, find the Z-score for my marathon time.

2. Is my marathon finishing time of 170 minutes unusually fast? Explain your answer using the Z-score.

This data set is a sample of the average number of hours per year that a driver is delayed by road congestion in 11 cities:

1. Find the mean and the standard deviation, including units.

2. What is the Z-score for the city with an average delay time of 42 hours per year?

In a survey of 12 companies recruiting for recent college graduates, they reported the following numbers of job applicants per job posting:

1. Find the mean and standard deviation, including units.

2. What is the Z score for the company with 143 job applicants per job posting?

You scored an 89 on a math test where the class mean and standard deviation are 75 points and 7 points respectively. You scored a 65 on an English test where the mean and standard deviation are 53 points and 4 points, respectively. In which class did you do better? Explain your answer using Z-scores.

The mean running time for comedy movies is 139 minutes, with a standard deviation of 39.7 minutes. For action movies, the mean running time is 159 minutes, with a standard deviation of 26.2 minutes. A recent comedy movie had a running time of 102 minutes, while an action movie playing at the same theatre had a running time of 129 minutes. Which movie is shorter compared to other movies in the same…

Poe, the Clydesdale horse has a world record breaking height of 20.2 hands. All Clydesdale horses have a mean height of 16.5 hands and a standard deviation of 1.85 hands. The last Great Dane to hold the world record for dog height was Gibson who was 107 cm tall. Great Danes have a mean height of 81 cm and a standard deviation of 13 cm. Which animal is taller compared to their respective breed? Exp…