Question

STEM experiences for girls. The National Science Foundation (NSF) sponsored a study on girls’ 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—c 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

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.
5. 
   

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

g.

Step-by-step solution

Determining the proportion of women from urban areas

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

$$\begin{gathered} \mathbf{\text{Proportion =}}\frac{\mathbf{\text{Number}}\mathbf{ }\mathbf{\text{of}}\mathbf{ }\mathbf{\text{women}}\mathbf{ }\mathbf{\text{from}}\mathbf{ }\mathbf{\text{urban}}\mathbf{ }\mathbf{\text{areas}}}{\mathbf{\text{Total}}\mathbf{ }\mathbf{\text{number}}\mathbf{ }\mathbf{\text{of}}\mathbf{ }\mathbf{\text{women}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=}}\frac{\mathbf{\text{107}}}{\mathbf{\text{174}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{= 0.614}} \end{gathered}$$

Identifying the proportion of women from suburban areas

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

$$\begin{gathered} \mathbf{\text{Proportion =}}\frac{\mathbf{\text{Number}}\mathbf{ }\mathbf{\text{of}}\mathbf{ }\mathbf{\text{women}}\mathbf{ }\mathbf{\text{from}}\mathbf{ }\mathbf{\text{suburban}}\mathbf{ }\mathbf{\text{areas}}}{\mathbf{\text{Total}}\mathbf{ }\mathbf{\text{number}}\mathbf{ }\mathbf{\text{of}}\mathbf{ }\mathbf{\text{women}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=}}\frac{\mathbf{\text{57}}}{\mathbf{\text{174}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{= 0.328}} \end{gathered}$$

Identifying the proportion of women from rural areas

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

$$\begin{gathered} \mathbf{\text{Proportion =}}\frac{\mathbf{\text{Number}}\mathbf{ }\mathbf{\text{of}}\mathbf{ }\mathbf{\text{women}}\mathbf{ }\mathbf{\text{from}}\mathbf{ }\mathbf{\text{rural}}\mathbf{ }\mathbf{\text{areas}}}{\mathbf{\text{Total}}\mathbf{ }\mathbf{\text{number}}\mathbf{ }\mathbf{\text{of}}\mathbf{ }\mathbf{\text{women}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{=}}\frac{\mathbf{\text{10}}}{\mathbf{\text{174}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\text{= 0.058}} \end{gathered}$$

Converting the proportions into degrees

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

$$\begin{gathered} \mathit{F}\mathit{o}\mathit{r}\mathbf{}\mathit{u}\mathit{r}\mathit{b}\mathit{a}\mathit{n}\mathbf{}\mathit{a}\mathit{r}\mathit{e}\mathit{a}\mathit{s}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{614}\mathbf{}\mathbf{\times }\mathbf{360} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}{\mathbf{\text{= 221.04}}}^{\mathbf{o}} \\ \mathit{F}\mathit{o}\mathit{r}\mathbf{}\mathit{s}\mathit{u}\mathit{b}\mathit{u}\mathit{r}\mathit{b}\mathit{a}\mathit{n}\mathbf{}\mathit{a}\mathit{r}\mathit{e}\mathit{a}\mathit{s}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{328}\mathbf{\times }\mathbf{360} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}{\mathbf{\text{= 118.08}}}^{\mathbf{o}} \\ \mathit{F}\mathit{o}\mathit{r}\mathbf{}\mathit{r}\mathit{u}\mathit{r}\mathit{a}\mathit{l}\mathbf{}\mathit{a}\mathit{r}\mathit{e}\mathit{a}\mathit{s}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{058}\mathbf{}\mathbf{\times }\mathbf{360} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}{\mathbf{\text{= 20.88}}}^{\mathbf{o}} \end{gathered}$$

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.

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.

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.