2.3 Measures of the Location of the Data

For the following 13 real estate prices, calculate the IQR and determine if any prices are potential outliers. Prices are in dollars.
389,950; 230,500; 158,000; 479,000; 639,000; 114,950; 5,500,000; 387,000; 659,000; 529,000; 575,000; 488,800; 1,095,000

For the 11 salaries, calculate the IQR and determine if any salaries are outliers. The following salaries are in dollars.

1. $33,000
2. $64,500
3. $28,000
4. $54,000
5. $72,000
6. $68,500
7. $69,000
8. $42,000
9. $54,000
10. $120,000
11. $40,500

Find the interquartile range for the following two data sets and compare them.

Test Scores for Class A:
69, 96, 81, 79, 65, 76, 83, 99, 89, 67, 90, 77, 85, 98, 66, 91, 77, 69, 80, 94
Test Scores for Class B:
90, 72, 80, 92, 90, 97, 92, 75, 79, 68, 70, 80, 99, 95, 78, 73, 71, 68, 95, 100

Forty bus drivers were asked how many hours they spend each day running their routes (rounded to the nearest hour). Find the 65^th percentile.

Using the table:

1. Find the 80^th percentile.
2. Find the 90^th percentile.
3. Find the first quartile. What is another name for the first quartile?

Refer to the table. Find the third quartile. What is another name for the third quartile?

Listed are 29 ages for Academy Award-winning best actors in order from smallest to largest:
18, 21, 22, 25, 26, 27, 29, 30, 31, 33, 36, 37, 41, 42, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77

1. Find the 70^th percentile.
2. Find the 83^rd percentile.

Listed are 29 ages for Academy Award-winning best actors in order from smallest to largest:

18, 21, 22, 25, 26, 27, 29, 30, 31, 33, 36, 37, 41, 42, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77
Calculate the 20^th percentile and the 55^th percentile.

Listed are 29 ages for Academy Award-winning best actors in order from smallest to largest:
18, 21, 22, 25, 26, 27, 29, 30, 31, 33, 36, 37, 41, 42, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77

1. Find the percentile for 58.
2. Find the percentile for 25.

Listed are 30 ages for Academy Award-winning best actors in order from smallest to largest:

18, 21, 22, 25, 26, 27, 29, 30, 31, 31, 33, 36, 37, 41, 42, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77
Find the percentiles for 47 and 31.

On a timed math test, the first quartile for time it took to finish the exam was 35 minutes. Interpret the first quartile in the context of this situation.

For the 100-meter dash, the third quartile for times for finishing the race was 11.5 seconds. Interpret the third quartile in the context of the situation.

On a 20-question math test, the 70^th percentile for number of correct answers was 16. Interpret the 70^th percentile in the context of this situation.

On a 60-point written assignment, the 80^th percentile for the number of points earned was 49. Interpret the 80^th percentile in the context of this situation.

At a high school, it was found that the 30^th percentile of number of hours that students spend studying per week is seven hours. Interpret the 30^th percentile in the context of this situation.

During a season, the 40^th percentile for points scored per player in a game is eight. Interpret the 40^th percentile in the context of this situation.

Listed are 29 ages for Academy Award-winning best actors in order from smallest to largest:

18, 21, 22, 25, 26, 27, 29, 30, 31, 33, 36, 37, 41, 42, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77

1. Find the 40^th percentile.
2. Find the 78^th percentile.

Jesse was ranked 37^th in his graduating class of 180 students. At what percentile is Jesse’s ranking?

1. For runners in a race, a higher speed means a faster run. Is it more desirable to have a speed with a high or a low percentile when running a race?
2. The 40^th percentile of speeds in a particular race is 7.5 miles per hour. Write a sentence interpreting the 40^th percentile in the context of the situation.

Mina is waiting in line at the Department of Motor Vehicles. Her wait time of 32 minutes is the 85^th percentile of wait times. Is that good or bad? Write a sentence interpreting the 85^th percentile in the context of this situation.

In a study collecting data about the repair costs of damage to automobiles in a certain type of crash tests, a certain model of car had $1,700 in damage and was in the 90^th percentile. Should the manufacturer and the consumer be pleased or upset by this result? Explain and write a sentence that interprets the 90^th percentile in the context of this problem.

Suppose that you are buying a house. You and your real estate agent have determined that the most expensive house you can afford is the 34^th percentile. The 34^th percentile of housing prices is $240,000 in the town you want to move to. In this town, can you afford 34 percent of the houses or 66 percent of the houses?

Use the exercise to calculate the following values.

Second quartile = median = 50^th percentile = ________

Use the exercise to calculate the following values.

Interquartile range (IQR) = ________ – ________ = ________

Use the exercise to calculate the following values.

70^th percentile = ________

Six hundred adult Americans were asked by telephone poll, "What do you think constitutes a middle-class income?" The results are in the table. Also, include the left endpoint but not the right endpoint.

1. What percentage of the survey answered "not sure"?
2. What percentage think that middle class is from $25,000 to $50,000?
3. Construct a histogram of the data.
   1. Should all bars have the same width, based…