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Data from Microsoft Bookshelf.
King, Bill.“Graphically Speaking.” Institutional Research, Lake Tahoe Community College. Available online at http://www.ltcc.edu/web/about/institutional-research (accessed April 3, 2013).
The standard deviation can help you calculate the spread of data. There are different equations to use if are calculating the standard deviation of a sample or of a population.
${s}_{x}=\sqrt{\frac{{\displaystyle \sum f{m}^{2}}}{n}-{\overline{x}}^{2}}$ where $\begin{array}{l}{s}_{x}=\text{samplestandarddeviation}\\ \overline{x}\text{=samplemean}\end{array}$
Use the following information to answer the next two exercises : The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles.
29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150
Use a graphing calculator or computer to find the standard deviation and round to the nearest tenth.
s = 34.5
Find the value that is one standard deviation below the mean.
Two baseball players, Fredo and Karl, on different teams wanted to find out who had the higher batting average when compared to his team. Which baseball player had the higher batting average when compared to his team?
Baseball Player | Batting Average | Team Batting Average | Team Standard Deviation |
---|---|---|---|
Fredo | 0.158 | 0.166 | 0.012 |
Karl | 0.177 | 0.189 | 0.015 |
For Fredo: z = $\frac{0.158\text{\u2013}0.166}{0.012}$ = –0.67
For Karl: z = $\frac{0.177\text{\u2013}0.189}{0.015}$ = –0.8
Fredo’s z -score of –0.67 is higher than Karl’s z -score of –0.8. For batting average, higher values are better, so Fredo has a better batting average compared to his team.
Use [link] to find the value that is three standard deviations:
Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83/84 .
Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83/84.
Grade | Frequency |
---|---|
49.5–59.5 | 2 |
59.5–69.5 | 3 |
69.5–79.5 | 8 |
79.5–89.5 | 12 |
89.5–99.5 | 5 |
Daily Low Temperature | Frequency |
---|---|
49.5–59.5 | 53 |
59.5–69.5 | 32 |
69.5–79.5 | 15 |
79.5–89.5 | 1 |
89.5–99.5 | 0 |
Points per Game | Frequency |
---|---|
49.5–59.5 | 14 |
59.5–69.5 | 32 |
69.5–79.5 | 15 |
79.5–89.5 | 23 |
89.5–99.5 | 2 |
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