National Park Road Trip: Beyond the Average

Use center and variation to interpret a travel journal.

Answer Key

1. Read the Travel Journal

Use the recorded driving distances. A measure of center describes a typical value with one number. A measure of variation describes how much the values differ.

Five Driving Days Between National Park Stops
Day	Miles driven
1	60
2	80
3	100
4	120
5	140

The journal's mean driving distance is 100 miles per day. Which use of 100 matches its role as a measure of center?

A. Use 100 miles as the average distance of the values from their mean.
B. Use 100 miles as a single representative daily driving distance.
C. Use 100 miles as the difference between the longest and shortest days.
D. Use 100 miles as the distance driven on every recorded day.

One measure of variation is mean absolute deviation (MAD). Find each value's distance from the mean, then average those distances. Distances are never negative.

The mean is 100 miles. Complete the distances from the mean for the first and last driving days.

Day 1: 40 miles from the mean; Day 5: 40 miles from the mean.

For the five driving days, the distances from the mean are 40, 20, 0, 20, and 40 miles. Average these distances to find the MAD.

MAD = 24 miles

What does a MAD of 24 miles mean for these driving days?

A. The daily distances differ by 24 miles from shortest to longest.
B. The daily distances are all exactly 24 miles away from the mean.
C. The daily distances have a mean of 24 miles per day.
D. The daily distances are an average of 24 miles away from the mean.

Sam subtracts the mean from each distance: −40, −20, 0, 20, and 40. These differences average to 0. Why should Sam not report 0 as the MAD?

A. The zero difference must be removed before averaging.
B. The mean must be replaced by the greatest driving distance.
C. The differences must be divided by the mean driving distance.
D. The distances must be nonnegative so they do not cancel.

2. Make Planning Decisions

Use each summary for the question it can actually answer. A smaller MAD means the recorded values stayed closer to their own mean on average.

A family compares two proposed routes across national parks. They prefer shorter driving days on average, even if the daily distances vary more. Which plan matches that priority?

Proposed Driving Plans
Plan	Mean daily miles	MAD in miles
Canyon	90	30
Forest	110	10

A. Choose Canyon because its MAD is larger.
B. Choose Forest because its mean is larger.
C. Choose Canyon because its mean is smaller.
D. Choose Forest because its MAD is smaller.

At a park entrance, the family records waiting times. Select the two questions that require information about variation, not just center.

How far from the average were the waiting times, on average?What was the middle waiting time when the times were ordered?Were the waiting times tightly grouped or widely spread?What was the average waiting time for an entrance visit?

A scenic shuttle's waiting times have a median of 12 minutes and a MAD of 4 minutes. Which number should the family use as a summary of a typical wait?

A. Use 12 minutes, the measure of center.
B. Use 16 minutes, the sum of the summaries.
C. Use 4 minutes, the measure of variation.
D. Use 8 minutes, the difference of the summaries.

The family needs fuel stops at fairly regular distances. Their notes summarize the miles between stops on two roads. Which conclusion follows from the summaries?

Distances Between Fuel Stops
Road	Mean miles	MAD in miles
Mesa Road	50	6
Ridge Road	50	18

A. Ridge Road has a larger typical distance between stops.
B. Ridge Road's distances stay closer to their mean on average.
C. Mesa Road's distances stay closer to their mean on average.
D. Mesa Road has a smaller typical distance between stops.

10.

A visitor center reports a mean parking-search time of 8 minutes and a MAD of 2 minutes. Elena concludes that no search took more than 10 minutes. What should she check?

A. Check the longest time; MAD is not a maximum distance.
B. Check the MAD; it always equals the longest search.
C. Check the mean; adding 2 always gives the longest search.
D. Check the median; it always equals the longest search.

3. Check What Summaries Tell You

Distinguish the location of the data from how much the values differ. Explain your reasoning in the final question.

11.

The family takes four ranger-led walks lasting 35, 35, 35, and 35 minutes. The mean is 35 minutes. Find the MAD to describe the variation.

MAD = 0 minutes

12.

The trip journal lists a MAD of 0 miles for three driving days, but the mean is hidden. Which statement is justified?

A. The family drove 0 miles on each of the three days.
B. The family drove the same distance on all three days.
C. The family's total distance was 3 miles for those days.
D. The family's distances increased by 3 miles each day.

13.

A travel report says, “The mean length of our park visits was 5 hours, and the MAD was 1 hour.” Select the two edits that correctly label what these numbers summarize.

Label 5 hours as the center of the visit lengths.Label 1 hour as the center of the visit lengths.Label 5 hours as the variation in the visit lengths.Label 1 hour as the variation in the visit lengths.

14.

A travel-journal app has two boxes: “Typical daily distance” and “Variation in daily distance.” Jordan enters “100 miles” in both boxes because the five daily distances were 100, 100, 100, 100, and 100 miles. Explain which entry should change and why. Use MAD for variation.

The typical daily distance can stay 100 miles because the mean is 100 miles. The variation entry should change to 0 miles. Every distance is equal to the mean, so every distance from the mean is 0 and the MAD is 0. A large center does not mean large variation.