



${s}_{x}=\sqrt{\frac{{\displaystyle \sum f{m}^{2}}}{n}{\overline{x}}^{2}}$ 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
Frequency is the number of all object which is comes from population or sample size
Faiqa
number of all objects?
Amir
frequency is the rate of occurrence of an object
Leek
Explain nominal and ordinal variables
Oyinlola
nominal variables are those variable which is used to “name,” a series of values.
Amir
while ordinal scales provide good information about the order of choices,for example in a customer satisfaction survey.
Amir
what is the difference between Mean and Varience?
Amir
Sum of total object, divided by number of object is called mean
Faiqa
faiqa U didn't clear me.Sorry
Amir
what is df in statistics
Oyinlola
Acquits the accused when in fact,he is ennocent
statistics is a mathematical sciences which deals with collection,presentation and analysis the numerical data
CH
statistics is a tools who convert data into information
CH
method of collection of data
problems of find mean and standard deviation with drawing curve
describe the methods of calculation of sample
what are the various uses of statistics in education
Survey, Public allocation of federal funds, business analysis and consumer data, the lotto, government programs and special services.
Willard
dicuss probability sampling
Rosy
given that a sample is normally distributed with M=10 sd=8 determine
Rosy
disscuss probability sampling
Rosy
Discuss probability sampling
Rosy
Probability sampling is based on the fact that every member of a population has a known and equal chance of being selected. For example, if you had a population of 100 people, each person would have odds of 1 out of 100 of being chosen. With nonprobability sampling, those odds are not equal.
Willard
The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.
To calculate it:
• add up all the numbers,
• then divide by how many numbers there are.
Example: what is the mean of 2, 7 and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers, 3
you
Willard
guidelines of designing a table
Anuradha
you can find that information on this website there is a lot of information. It's about interpreting what the concept of information & data you are getting from the graph and understanding how to read the graph and analyze the information. ***understandinggraphics.com/design/datatabledesign/
Willard
find X and Y so that the ordered data set has a mean of 38 and median of 35
17, 22, 26, 29, 34, X, 42, 67 , 70, Y
Mohamed
Write short notes on, nominal variable, ordinal variable, internal variable, ratio variable.
olusola
P( /x50/ less than or equal to 5 ) where mean =52 and Variance =25
please what is data mining
the exploration and analysis of large data to discover meaningful patterns and rules
Hussein
how do we calculate the median
f(x)=cx(1x)^4 as x range 4rm 0<=x<=1. Can someone pls help me find d constant C. By integration only..
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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