12.9: Chapter 9 Exercise Solutions
- Page ID
- 60003
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Chapter 9: Statistics, Describing Data.
1. a. Different tables are possible
| Score | Frequency |
| 30 | 1 |
| 40 | 0 |
| 50 | 4 |
| 60 | 3 |
| 70 | 6 |
| 80 | 5 |
| 90 | 2 |
| 100 | 3 |
b. This is technically a bar graph, not a histogram:
c. 
3. a. \(5+3+4+2+1 = 15\)
b. \(\dfrac{5}{15} = 0.3333 = 33.33 \%\)
5. Bar is at \(25 \%\). \(25 \%\) of \(20 = 5\) students earned an A
7. a. \(\dfrac{(7.25+8.25+9.00+8.00+7.25+7.50+8.00+7.00)}{8} = $7.781\)
b. In order, \(7.50\) and \(8.00\) are in middle positions. Median \(= $7.75\)
c. \(0.25 \times 8 = 2\). Q1 is average of \(2^{\text{nd}}\) and \(3^{\text{rd}}\) data values: \($7.375\)
\(0.75 \times 8 = 6\). Q3 is average of \(6^{\text{th}}\) and \(7^{\text{th}}\) data values: \($8.125\)
5-number summary: \($7.00, $7.375, $7.75, $8.125, $9.00\)
9. a. \(\dfrac{((5 \times 0) + (3 \times 1) + (4 \times 2) + (2 \times 3) + (1 \times 5))}{15} = 1.4667\)
b. Median is \(8^{\text{th}}\) data value: \(1\) child
c. \(0.25 \times 15 = 3.75\). Q1 is \(4^{\text{th}}\) data value: \(0\) children
\(0.75 \times 15 = 11.25\). Q3 is \(12^{\text{th}}\) data value: \(2\) children
5-number summary: \(0, 0, 1, 2, 5\)
d. 
11. Kendra makes \($90,000\). Kelsey makes \($40,000\). Kendra makes \($50,000\) more.