



${s}_{x}=\sqrt{\frac{{\displaystyle \sum f{m}^{2}}}{n}{\overline{x}}^{2}}$ 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
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.
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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 

${s}_{x}=\sqrt{\frac{{\displaystyle \sum f{m}^{2}}}{n}{\overline{x}}^{2}}=\sqrt{\frac{193157.45}{30}{79.5}^{2}}=10.88$

${s}_{x}=\sqrt{\frac{{\displaystyle \sum f{m}^{2}}}{n}{\overline{x}}^{2}}=\sqrt{\frac{380945.3}{101}{60.94}^{2}}=7.62$

${s}_{x}=\sqrt{\frac{{\displaystyle \sum f{m}^{2}}}{n}{\overline{x}}^{2}}=\sqrt{\frac{440051.5}{86}{70.66}^{2}}=11.14$
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Bringing it together
Twentyfive randomly selected students were asked the number of movies they watched the previous week. The results are as follows:
# of movies 
Frequency 
0 
5 
1 
9 
2 
6 
3 
4 
4 
1 
 Find the sample mean
$\overline{x}$ .
 Find the approximate sample standard deviation,
s .
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Forty randomly selected students were asked the number of pairs of sneakers they owned. Let
X = the number of pairs of sneakers owned. The results are as follows:
X 
Frequency 
1 
2 
2 
5 
3 
8 
4 
12 
5 
12 
6 
0 
7 
1 
 Find the sample mean
$\overline{x}$
 Find the sample standard deviation,
s
 Construct a histogram of the data.
 Complete the columns of the chart.
 Find the first quartile.
 Find the median.
 Find the third quartile.
 Construct a box plot of the data.
 What percent of the students owned at least five pairs?
 Find the 40
^{th} percentile.
 Find the 90
^{th} percentile.
 Construct a line graph of the data
 Construct a stemplot of the data
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Following are the published weights (in pounds) of all of the team members of the San Francisco 49ers from a previous year.
177; 205; 210; 210; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174; 185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270; 280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215; 185; 230; 250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265
 Organize the data from smallest to largest value.
 Find the median.
 Find the first quartile.
 Find the third quartile.
 Construct a box plot of the data.
 The middle 50% of the weights are from _______ to _______.
 If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why?
 If our population included every team member who ever played for the San Francisco 49ers, would the above data be a sample of weights or the population of weights? Why?
 Assume the population was the San Francisco 49ers. Find:
 the population mean,
μ .
 the population standard deviation,
σ .
 the weight that is two standard deviations below the mean.
 When Steve Young, quarterback, played football, he weighed 205 pounds. How many standard deviations above or below the mean was he?
 That same year, the mean weight for the Dallas Cowboys was 240.08 pounds with a standard deviation of 44.38 pounds. Emmit Smith weighed in at 209 pounds. With respect to his team, who was lighter, Smith or Young? How did you determine your answer?
 174; 177; 178; 184; 185; 185; 185; 185; 188; 190; 200; 205; 205; 206; 210; 210; 210; 212; 212; 215; 215; 220; 223; 228; 230; 232; 241; 241; 242; 245; 247; 250; 250; 259; 260; 260; 265; 265; 270; 272; 273; 275; 276; 278; 280; 280; 285; 285; 286; 290; 290; 295; 302
 241
 205.5
 272.5

 205.5, 272.5
 sample
 population

 236.34
 37.50
 161.34
 0.84 std. dev. below the mean
 Young
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Questions & Answers
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The mode of the density of power of signal is 3.5. Find the probability that the density of a random signal will be more than 2.5.
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A quality control specialist took a random sample of n = 10 pieces of gum and measured their thickness and found the mean 9 and variance 0.04. Do you think that the mean thickness of the spearmint gum it produces is 8.4
3. The following are the number of mails received in different days by different organizations:
Days (x) : 23, 35, 38, 50, 34, 60, 41, 32, 53, 67.
Number of mails (y) : 18, 40, 52, 45, 32, 55, 50, 48, 26, 25.
i) Fit a regression line of y on x and test the significance of regression.
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The number of problem creating computers of two laboratories are as follows:
Number of computers: 48, 6, 10, 12, 30, 11, 49, 17, 10, 14, 38, 25, 15, 19, 40, 12.
Number of computers: 12, 10, 26, 11, 42, 11, 13, 12, 18, 5, 14, 38.
Are the two laboratories similar in respect of problem creating compute
Is the severity of the drug problem in high school the same for boys and
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a quality control specialist took a random sample of n=10 pieces of gum and measured their thickness and found the mean 7.6 and standered deviation 0.10. Do you think that the mean thickness of the spearmint gum it produces is 7.5?
99. A one sample, onetail ttest is conducted and the test statistic value is calculated to be 2.56.
The degrees of freedom for the test are 10. Which of the following conclusions for the test would
be correct?
a
A one sample, onetail ttest is conducted and the test statistic value is calculated to be 2.56.
The degrees of freedom for the test are 10. Which of the following conclusions for the test would
be correct?
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Worthy
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Jungjoon
I'm struggling to type it's on my laptop...statistics
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types of averages .mean median mode quarantiles MCQ question
Out of 25 students, 15 are male. Is the overall proportion of male students 0.7 in AIUB?
(4 Points)
15/25=0.6 or 60% standard calculation
Andrea
A quality control specialist took a random sample of n = 10 pieces of gum and measured their thickness and found the mean 7.6 and variance 0.01. Do you think that the mean thickness of the spearmint gum it produces is 7.5?
(4 Points)
Omer
10 gums
mean = 7.6
variance= 0.01
standard deviation= ?
what us the data set?
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A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Twelve older adults (over the age of 50) and twelve younger adults (between 20 and 40) were given a life satisfaction tes
Source:
OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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