2.9: Descriptive Statistics (Worksheet)
- Page ID
- 40371
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Work in groups on these problems. You should try to answer the questions without referring to your notes. If you get stuck, try asking another group for help.
Student Learning Outcomes
- The student will organize and construct visual displays of qualitative and quantitative data.
- The student will calculate univariate descriptive statistics.
- The student will analyze graphs and numeric summaries to interpret what the data implies.
The Data
The table contains data from a 2014 African Financial Survey on a random sample of 18 African countries. The four columns provide the following information:
- Country
- Region - which region of the continent the country is in: North, East, South, West, Central
- Inflation Rate - the inflation rate of the country in 2014, reported as a %
- No. of Bank Branches - the number of bank branches in 2014 located in the country
| Country | Region | Inflation Rate | No. Bank Branches |
|---|---|---|---|
| Algeria | North Africa | 4.24 | 1438 |
| Cameroon | Central Africa | 2.45 | 185 |
| Cote d'Ivoire | West Africa | 2.86 | 600 |
| Equatorial Guinea | Central Africa | 5.83 | 15 |
| Ethiopia | East Africa | 7.89 | 2208 |
| Gabon | Central Africa | 2.67 | 58 |
| Ghana | West Africa | 9.89 | 967 |
| Lesotho | Southern Africa | 4.94 | 46 |
| Madagascar | Southern Africa | 7.2 | 233 |
| Mali | West Africa | 2.07 | 516 |
| Mauritius | Southern Africa | 3.61 | 223 |
| Namibia | Southern Africa | 5.78 | 111 |
| Rwanda | East Africa | 4.44 | 161 |
| Seychelles | East Africa | 4.17 | 30 |
| South Africa | Southern Africa | 5.68 | 3697 |
| Swaziland | Southern Africa | 5.95 | 49 |
| Togo | West Africa | 2.27 | 200 |
| Zimbabwe | Southern Africa | 3.97 | 742 |
Organize the Data
For each of the three variables - Region, Inflation Rate, No. Bank Branches - complete each of the following steps.
- Identify the variable type: qualitative, quantitative - discrete, quantitative - continuous.
- Construct a frequency distribution table.
- Visualize the frequency distribution with either a bar graph, pie chart, or histogram. Be sure to select the most appropriate visual display for the variable type.
- Describe the shape of the distribution.
- Are there any potential outliers? List the value(s) that could be outliers. Use a formula to check the end values to determine if they are potential outliers.
Analyze the Data
- Determine the appropriate measure of center for the variable Region. Can a measure of variation be computed for this variable
- For the variable Inflation Rate, determine each of the following.
- measures of center: mean, median, mode
- measures of variation: range, variance, sd
- 5-number summary
- outliers
- Comment on which measure of center and which measure of variation is most appropriate.
- Repeat the steps in #2. for the variable No. Bank Branches.
Interpret the Data
Write a few sentences to indicate what information is included in the sample. Consider commenting on which region is most represented in the data, what the typical inflation rate is, and what the typical number of bank branches is based on this sample. Add any other insights you noticed in analyzing the data.