# Descriptive Statistics

15.

A doctor's office staff studied the waiting times for patients who arrive at the office with a request for emergency service. The following data with waiting times in minutes were collected over a one-month period.

2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3

Use classes of 0-4, 5-0 and so in the following:

A. Show the frequency distribution

B. Show the relative frequency distribution

c. Show the cumulative frequency distribution.

d. Show the cumulative relative frequency distribution.

e. what proportion of patients needing emergency service wait 9 minutes or less?

Scenario.

3.

A small company was trying to determine the amount of the average order for parts. It had received over 1000 orders for parts. The office manager had the computer select 35 of those orders randomly. He determined that the mean amount of these 35 orders was $389.45 One of the orders was for $350 in miscellaneous cables. He informed his boss that he was 95% certain that the average order that they had received was between $337.97 and $441.03.

1. Determine what is the sample

2. state what is the population

3. identify one or more variables

4. determine if each variable is quantitative or qualitative and if the scale is nominal, ordinal, interval, or ratio

5. find one piece of datum

6. find a statistic, and

7. find a parameter.

1. Consider a sample with data values of 10, 20, 17, and 16. Compute the mean and median.

3.3 13. Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the range and interquartile range.

17. A home theater in a box is the easiest and cheapest way to provide surround sound for a home entertainment center. A sample of prices is shown here (Consumer Reports Buying Guide, 2004) The prices are for models with a DVD player and for models without a DVD player.

Model with DVD player price ($) Models without a DVD player Price ($)

Sony HT-1800DP 450 Pioneer HTP-230 300

Pioneer HTD-330DV 300 Sony HT-DDW750 300

Sony HT-C800DP 400 Kenwood HTB-306 360

Panasonic SC-HT900 500 RCA RT-2600 290

Panasonic SC-MTI 400 Kenwood HTB-206 300

a. compute the mean price for models with a dvd player and the mean price for models without a dvd player. What is the additional price paid to have a DVD player included in a home theater unit?

B. compute the range, variance, and standard deviation for the two samples. What does this information tell you about the prices for models with and without a DVD player?

19. The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A sample of air quality index values for Pomona provided the following data: 28, 42, 45, 55, 60, 49, and 50.

A compute the range and interquartile range

B. compute the sample variance and sample standard deviation.

C. A sample of air quality index readings for Anaheim provided a sample mean 48.5, a sample variance of 136, and a sample standard deviation of 11.66. What comparisons can you make between the air quality in Pomona and that in Anaheim on the basis of these descriptive statistics.

#### Solution Preview

Please see the attached file.

15.

A doctor's office staff studied the waiting times for patients who arrive at the office with a request for emergency service. The following data with waiting times in minutes were collected over a one-month period.

2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3

Use classes of 0-4, 5-0 and so in the following:

Class Frequency Cum. Freq Rel. Freq Rel Cum. Freq

0-5 6 6 0.3 0.3

5-10 7 13 0.35 0.65

10-15 4 17 0.2 0.85

15-20 2 19 0.1 0.95

20-25 1 20 0.05 1

Total 20

A. Show the frequency distribution

See above table

B. Show the relative frequency distribution

See above table

c. Show the cumulative frequency distribution.

See above table

d. Show the cumulative relative frequency distribution.

See above table

e. what proportion of patients needing emergency service wait 9 minutes or less?

Number of patients who wait 9 min or less = 12

Total observations = 20

Proportion of patients needing emergency service waits 9 minutes or less

= 12/20 *100

= 60%

Scenario.

3.

A small company was trying to determine the amount of the average order for parts. It had received over 1000 orders for parts. The office manager had the computer select 35 of those orders randomly. He determined that the mean amount of these 35 orders was $389.45 One of the orders was for $350 in miscellaneous cables. He informed his boss that he was 95% certain that the average order that they had received was between $337.97 and $441.03.

1. Determine what is the sample

The randomly selected 35 orders

2. state what is the population

The set of all 1000 orders

3. Identify one or more variables

Amount for ...

#### Solution Summary

The solution gives the step by step procedure for the definitions and calculation of mean, median, mode, cumulative frequency, relative frequency and standard deviation.