Skip to main content
Mathematics LibreTexts

14.6.1: Describing Data

  • Page ID
    110138
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    1.

    1. Different tables are possible

    \(\begin{array}{|l|l|}
    \hline \text { Score } & \text { Frequency } \\
    \hline 30 & 1 \\
    \hline 40 & 0 \\
    \hline 50 & 4 \\
    \hline 60 & 3 \\
    \hline 70 & 6 \\
    \hline 80 & 5 \\
    \hline 90 & 2 \\
    \hline 100 & 3 \\
    \hline
    \end{array}\)

    1. This is technically a bar graph, not a histogram:

    clipboard_ea99cefb4a8bc3d6c75c46cd897e990c1.png

    clipboard_e0fcb81c339f46050406fc822de454710.png

    3.

    1. \(5+3+4+2+1=15\)
    2. \(5 / 15=0.3333=33.33 \%\)

    5. Bar is at \(25 \% .25 \%\) of \(20=5\) students earned an \(A\)

    7.

    1. \((7.25+8.25+9.00+8.00+7.25+7.50+8.00+7.00) / 8=\$ 7.781\)
    2. In order, 7.50 and 8.00 are in middle positions. Median \(=\$ 7.75\)
    3. \(0.25 * 8=2\) \(\mathrm{Q} 1\) is average of \(2^{\mathrm{nd}}\) and \(3^{\mathrm{rd}}\) data values: \(\$ 7.375 \quad 0.75 * 8=6 . \mathrm{Q} 3\) is average of \(6^{\mathrm{th}}\) and \(7^{\mathrm{th}}\) data values: \(\$ 8.125\) 5-number summary: \(\$ 7.00, \$ 7.375, \$ 7.75, \$ 8.125, \$ 9.00\)
    4. \(0.637\)

    9.

    1. \((5 \times 0+3 \times 1+4 \times 2+2 \times 3+1 \times 5) / 15=1.4667\)
    2. Median is 8th data value: 1 child
    3. \(0.25 \times 15=3.75 .\) Q1 is 4 \(^{\text {th}}\) data value: 0 children \(0.75 \times 15=11.25 .\) Q 3 is \(12^{\text {th}}\) data value: 2 children 5 -number summary: 0,0 1,2,5
    4. clipboard_e9f1f1ea7c3ee82b36ee6da2e01e6dacf.png

    11. Kendra makes $90,000. Kelsey makes $40,000. Kendra makes $50,000 more.


    This page titled 14.6.1: Describing Data is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Lippman (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

    • Was this article helpful?