# Frequency distribution, stem and leaf plot, statistical graphs

1. The acreage of the 39 U.S. National Parks under 900,000 acres (in thousands of acres) is shown here. Construct a frequency distribution for the data using eight classes. Do a frequency distribution, you are constructing a table, not a graph.

41 66 233 775 169

36 338 233 236 64

183 61 13 308 77

520 77 27 217 5

650 462 106 52 52

505 94 75 265 402

196 70 132 28 220

760 143 46 539

2. The data shown represent the percentage of unemployed males and females in the 1995 for a sample of countries of the world. Using the whole numbers as stems and the decimals as leaves, construct a back-to-back stem and leaf plot and compare the distributions of the two groups. Draw a graph. State one salient finding.

Females Males

8.0 3.7 8.6 5.0 7.0 8.8 1.9 5.6 4.6 1.5

3.3 8.6 3.2 8.8 6.8 2.2 5.6 3.1 5.9 6.6

9.2 5.9 7.2 4.6 5.6 9.8 8.7 6.0 5.2 5.6

5.3 7.7 8.0 8.7 0.5 4.4 9.6 6.6 6.0 0.3

6.5 3.4 3.0 9.4

3. State which graph (Pareto chart, time series graph or pie graph) would most appropriately represent the given:

a. The number of students enrolled at a local college for each year during the last 5 years.

b. The budget for the student activities department at a certain college for each year during the last 5 years.

c. The means of transportation the students use to get to school.

d. The percentage of votes each of the four candidates received in the last election.

e. The record temperatures of a city for the last years.

f. The frequency of each type of crime committed in a city during the year.

3. Make a graph. Then, answer the question. The number of successful space launches by the United States and Japan for the years 1993 - 1997 is shown here. Construct a compound time series graph for the data. What comparison can be made regarding the launches?

Year 1993 1994 1995 1996 1997

United States 29 27 24 32 37

Japan 1 4 4 1 2

4. Make a graph, then, describe the nature of the relationship. A researcher wishes to determine if there is a relationship between the number of days an employee missed a year and the person's age. Draw a scatter plot and comment on the nature of the relationship.

Age, x 22 30 25 35 65 50 27 53 42 58

Days missed, y 0 4 1 2 14 7 3 8 6 4

5. Draw a graph, then, describe the nature of the relationship. These data represent the ages of the drivers and the number of accidents reported for each age group in Pennsylvania for a selected year. Draw a scatter plot and describe the nature of the relationship.

Age,x 16 17 18 19 20 21

# of accidents, y 6605 8392 8506 7349 6458 5974

https://brainmass.com/statistics/time-series-analysis/frequency-distribution-stem-and-leaf-plot-statistical-graphs-83067

#### Solution Summary

This solution answers several statistical problems, for example about frequency distribution, stem and lead plots and various statistical graphs.

Statistical Analysis using Various Graphing Methods

1.

The data consists of a random sample of 50births taken from the 2007 North Carolina Birth Registry. For each variable:

(a)Group the data as indicated

(b) Prepare a frequency distribution with columns for intervals and frequencies

(c )Construct a histogram

Construct a frequency polygon

15 26 27 32 24 24 35 29 44 20

25 20 18 31 22 30 25 38 37 22

28 20 21 23 34 30 27 24 33 29

26 20 18 15 24 28 24 31 20 20

21 24 25 33 28 36 26 27 35 19

2.

Construct a frequency distribution and a histogram for the below monthly rent payments

430 330 740 860 940 280

2400 1000 1800 300 2400 300

2000 350 3200 2100 710 1100

1300 1100 500 500 2000 800

1000 160 1400 900 700 740

3.

For the 22 states that produce large numbers of broiler chickens, the following stem-and -leaf plot gives the production in millions of live pounds

a) Describe the shape of the distribution

b) How many states produce fewer than 10 million pounds

Stem Leaves

0 0012234

0 8

1 02333

1 66

2 2

3 2

3 4

4 78

5

5

6 4

6 7

Units:6/7 = 67 million pounds

4.

Construct a histogram and a frequency polygon for the following data.

Class Interval Frequency

30-under 32 5

32-under 34 7

34-under 36 15

36-under 38 21

38-under 40 34

40-under 42 24

42-under 44 17

44-under 46 8

5.

A list of the largest accounting firms the US along with their net revenue figures of 1997 ($millions) according to the Public Accounting Report follows.

Firm Revenue

Andersen Worldwide $5,445

Ernst&Young $4, 416

Deloitte&Touche $3,600

KPMG Peat Marwick $2,698

Coopers&Lybrand $2,504

PriceWaterhouse $2,344

Grant Thornton $289

McGladrey&Pullen $279

BDO Seidman $240

Construct a pie chart to represent these data. Label the slices with the appropriate percentages. Comment on the effectiveness of using a pie chart to display the revenue of these top accounting firms.

6.

An airline company uses a central telephone bank and a semi-automated telephone process to take reservations. It has been receiving an unusually high number of customer complaints about its reservation system. The company conducted a survey of customers, asking them whether they had encountered any of the following problems in making reservations: busy signal, disconnection, poor connection, too long a wait to talk to someone, could not get through to an agent, connected with the wrong person. Supposes a survey of 744 complaining customers resulted in the following frequency tally.

Number of Complaints Complaint

184 Too long a wait

10 Transferred to the wrong person

85 Could not get through to an agent

37 Got disconnected

420 Busy signal

8 Poor connection

Construct a Pareto diagram from this information to display the various problems encountered in making reservation.

7.

Are the advertising dollars spent by a company related to total sales revenue? The following data represent the advertising dollars and the sales revenues for various companies in a given industry during a recent year. Construct a scatter plot of the data from the two variables and discuss the relationship between the two variables.

Advertising (in $millions) Sales (in $millions)

4.2 155.7

1.6 87.3

6.3 135.6

2.7 99.0

10.4 168.2

7.1 136.9

5.5 101.4

8.3 158.2.