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STEM experiences for girls. The National Science Foundation (NSF) sponsored a study on girls鈥 participation in informal science, technology, engineering, or mathematics (STEM) programs. The results of the study were published in Cascading Influences: Long-Term Impacts of Informal STEM Experiences for Girls (March 2013). The researchers sampled 174 young women who recently participated in a STEM program. They used a pie chart to describe the geographic location (urban, suburban, or rural) of the STEM programs attended. Of the 174 STEM participants, 107 were in urban areas, 57 in suburban areas, and 10 in rural areas.

a. Determine the proportion of STEM participants from urban areas.

b. Determine the proportion of STEM participants from suburban areas.

c. Determine the proportion of STEM participants from rural areas.

d. Multiply each proportion in parts a鈥攃 by 360 to determine the pie slice size (in degrees) for each location.

e. Use the results, part d, to construct a pie chart for the geographic location of STEM participants.

f. Interpret the pie slice for urban areas.

g. Convert the pie chart into a bar graph. Which, in your opinion, is more informative?

Short Answer

Expert verified
  1. 0.614
  2. 0.328
  3. 0.058
  4. 221.04 degrees for urban areas, 118.08 for suburban areas, and 20.88 for rural areas.

f. It indicates that it acquires 61.4 percent area of the pie.

g.

Step by step solution

01

Determining the proportion of women from urban areas

The calculation of the proportion of women from the urban areas is presented below:

Proportion =NumberofwomenfromurbanareasTotalnumberofwomen=107174= 0.614

02

Identifying the proportion of women from suburban areas

The calculation of the proportion of women from the suburban areas is presented below:

Proportion =NumberofwomenfromsuburbanareasTotalnumberofwomen=57174= 0.328

03

Identifying the proportion of women from rural areas

The calculation of the proportion of women from the rural areas is presented below:

Proportion =NumberofwomenfromruralareasTotalnumberofwomen=10174= 0.058

04

Converting the proportions into degrees

The calculation of the proportion of women from each area in degrees are presented below:

Forurbanareas=0.614360= 221.04oForsuburbanareas=0.328360= 118.08oForruralareas=0.058360= 20.88o

05

Formatting the pie chart

By using the degrees calculated in Step 4, the pie chart has been formed representing the proportion (in degrees) of the number of participants in the STEM program. The largest pie slice represents the urban area and the smallest one represents the rural area.

06

Interpreting the pie slice for urban areas

The pie slice for urban areas is the largest one, indicating the maximum number of women is participating from the urban areas. 221.04 degrees indicates that 61.4 percent (0.614 has been multiplied by 100) of the total number of women are participating from the urban areas.

07

Providing opinion about bar graph and pie chart

Both pie charts and bar graphs are informative because both have a unique way of reflecting information. In the bar graph, the heights of the bars are taken into consideration, whereas, in the pie chart, it is the size of the slices.

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Most popular questions from this chapter

Monitoring weights of flour bags.When it is working properly, a machine that fills 25-pound bags of flour dispenses an average of 25 pounds per fill; the standard deviation of the amount of fill is .1 pound. To monitor the performance of the machine, an inspector weighs the contents of a bag coming off the machine鈥檚 conveyor belt every half hour during the day. If the contents of two consecutive bags fall more than 2 standard deviations from the mean (using the mean and standard deviation given above), the filling process is said to be out of control, and the machine is shut down briefly for adjustments. The data

given in the following table are the weights measured by the inspector yesterday. Assume the machine is never shut down for more than 15 minutes at a time. At what times yesterday was the process shut down for adjustment? Justify your answer.

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Performance ratings of government agencies.The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. A research team at George Mason University evaluated the quality of the PARS for 24 government agencies (The Public Manager, summer 2008). Evaluation scores ranged from 12 (lowest) to 60 (highest). The PARS evaluation scores for two consecutive years are shown in the next table.

a.Construct a scatterplot for the data. Do you detect atrend in the data?

b.Based on the graph, identify one or two agencies that hadgreater than expected PARS evaluation scores for year 2.

Calculate the mean for samples where

a.n=10,x=25b.n=16,x=400c.n=45,x=35d.n=18,x=242

Discuss the conditions under which the median is preferred to the mean as a measure of central tendency.

The Apprenticecontestants鈥 performance ratings.Refer to the Significance(April 2015) study of contestants鈥 performance on the popular TV show The Apprentice, Exercise 2.9 (p. 73). Recall that each of 159 contestants was rated (on a 20-point scale) based on their performance. The accompanying Minitab printout gives the mean and standard deviation of the contestant ratings, categorized by highest degree obtained (no degree, first degree, or postgraduate degree) and prize (job or partnership with Lord Sugar).

Descriptive Statistics: Ratings

Results for Prize = Job

Variable

Degree

N

Mean

StDev

Minimum

Maximum

Rating

First

54

7.796

4.231

1.000

17

None

35

7.457

4.388

1.000

20

Post

10

9.80

4.54

2.000

17

Results for Prize = Partnership

Variable

Degree

N

Mean

StDev

Minimum

Maximum

Rating

First

33

8.212

4.775

1.000

20.00

None

21

10.62

4.83

3.000

20.00

Post

6

6.50

3.33

2.000

12.00

a.Give a practical interpretation of the mean rating for contestants with a first (bachelor鈥檚) degree who competed for a job with Lord Sugar.

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