Algebra 2 CPName______
Stats Notes 1
EXAMPLE 1
Make a Stem and Leaf Plot for the following data set.
21, 18, 17, 18, 22, 46
a. What are the highest and lowest numbers?
b. What is the mean?
c. What is the median?
d. What is the mode?
e. What is the range of numbers?
EXAMPLE 2
Answer the questions based on the given Stem and Leaf Plot
a. What are the highest and lowest numbers?
b. What is the mean?
c. What is the median?
d. What is the mode?
e. What is the range of numbers?
EXAMPLE 3
Answer the questions based on the given Stem and Leaf Plot
a. What are the highest and lowest numbers?
b. What is the mean?
c. What is the median?
d. What is the mode?
e. What is the range of numbers?
EXAMPLE 4
The Stem and LeafPlot below shows the height (in feet) of buildings in San Francisco.
a. What are the highest and lowest numbers?
b. What is the mean?
c. What is the median?
d. What is the mode?
e. What is the range of numbers?
Algebra 2 CPName______
Stats Notes 2
EXAMPLE
Find the Five Number Summary, the Ranges, and the Outlier Fences for each of the following sets of data. If there are outliers, name them.
a. 13, 15, 25, 22, 18, 19
Outliers:______
b. 107, 57, 47, 40, 34, 20, 25, 37, 46, 57, 69
Outliers:______
c.
10 │ 1 represents 101
Outliers:______
d.
4 │ 7 represents 47
Outliers:______
Algebra 2 CPName______
Stats Notes 3
EXAMPLE 1
Answer each question for the box and whisker plot to the right
a. What are the upper and lower extremes?
b. What is the median?
c. What are the upper and lower quartiles?
d. What is the interquartile range?
EXAMPLE 2
Speeds of the fastest train runs in the U.S. and Canada are given below in miles per hour.
Make a box-and-whisker plot of this data.
93.582.589.583.881.886.8
90.884.995.083.183.288.2
EXAMPLE 3
Compare box and whisker plots A and B
a. What is the median of each data set?
b. What is the least value in plot A?
c. What is the greatest value in plot B?
d. Which plot has the greater interquartile range?
e. What is the lower quartile of each data set?
f. What is the upper quartile of each data set?
g. Which plot illustrates the larger range of data?
h. What percent of the data in plot A is greater than 60?
i. What percent of the data in plot B is less than 40?
EXAMPLE 4
Use the data to complete the following
22 23 27 22 33 47 24 25 33 37 28 28 17
a. Graph the data on a stem and leaf plot.b. Transfer the data to a vertical box and whisker plot
Stem / Leafc. What are the extremes?
d. What is the interquartile range?
e. Why are the whiskers unequal?
Algebra 2 CPName______
Stats Notes 4
The normal curve is a graphical representation of probability – otherwise known as the “bell curve”. There are several things to remember:
What does this all mean? Most outcomes will be within 3 standard deviations of the mean.
Standard Normal Table
Z / .0 / .1 / .2 / .3 / .4 / .5 / .6 / .7 / .8 / .9-3 / .0013 / .0010 / .0007 / .005 / .003 / .002 / .001 / .0001 / .0001 / .0000+
-2 / .0228 / .0179 / .0139 / .0107 / .0082 / .0062 / .0047 / .0035 / .0026 / .0019
-1 / .1587 / .1357 / .1151 / .0968 / .0808 / .0668 / .0548 / .0446 / .0359 / .0287
-0 / .5000 / .4602 / .4207 / .3821 / .3446 / .3085 / .2743 / .2420 / .2119 / .1841
0 / .5000 / .5398 / .5793 / .6179 / .6554 / .6915 / .7257 / .7580 / .7881 / .8159
1 / .8413 / .8643 / .8849 / .9032 / .9192 / .9332 / .9452 / .9554 / .9641 / .9713
2 / .9772 / .9821 / .9861 / .9893 / .9918 / .9938 / .9953 / .9965 / .9974 / .9981
3 / .9987 / .9990 / .9993 / .9995 / .9997 / .9998 / .9998 / .9999 / .9999 / 1.0000-
.0000+ means slightly more than 01.0000- means slightly less than 1
EXAMPLE 1– Using Normal Distribution Curves
Using the normal distribution identify the mean and the standard deviation
a.b.
EXAMPLE 2 – Using Your Calculator
Use the following information to calculate the mean and the standard deviation
a. 14, 15, 17, 17, 19, 21, 23b. 178, 193, 204, 211, 211, 216, 177, 173, 168
EXAMPLE 3 – Normal Distribution Percentages
What percentage is represented by the shaded region of the curve?
a.b.
EXAMPLE 4 – Creating a Normal Distribution
Use the following information to construct a normal distribution.
a. The math scores for the 2004 SAT are b. A group of women were found to have
normally distributed with a mean of 518 heights that are normally distributed
and a standard deviation of 114. with a mean of 64.5 inches and a
standard deviation of 2.5 inches.
EXAMPLE 5
Use the normal distributions you created in example 4 to answer the following questions.
a. What percentage of test takers have scoresb. What percentage of test takers have
within 2 standard deviations above the scores that are more than 1 standard
mean? below the mean?
c. What percentage of women are mored. What percentage of women are 1 or
than 3 standard deviations lower than more standard deviations above the
the mean? mean?
EXAMPLE 6 –Finding Z-Scores
Calculate the z –scores using the information from example 4 to answer the following questions.
a. What is the probability of scoring at mostb. What is the probability of having a
653 on the SAT? woman at most 70 inches tall?
Algebra 2 CPName______
11.4 NotesDate______
EXAMPLE 1 – Classify Samples
Determine the sample style portrayed in the following examples.
a. A manufacturer wants to sample the parts from a production line for defects.
- The manufacturer has every 5th item on the production line tested for defects
- The manufacturer has the first 50 items on the production line tested
b. A computer science teacher wants to know if students would like the morning announcements posted
on the school’s website.
- He surveys students in one of his computer science classes.
- He selects 50 names off of the master student list by closing his eyes and picking them from a hat
EXAMPLE 2 – Identify a Biased Sample
Determine whether or not the following samples are biased or unbiased and briefly explain why.
a. The manager of a concert hall wants to know how often people in the community attend concerts. The
manager asks 50 people standing in line for a rock concert how many concerts per year they attend.
b. A magazine asked its readers to send in their responses to several questions regarding healthy eating.
EXAMPLE 3 – Find a Margin of Error
a. In a survey of 1011 people, 52 % said that television is their main source of news.
A. What is the margin of error for the survey?
B. Give an interval that is likely to contain the exact percent of all people who use their television as
their main source of news
b. In a survey of 1535 people, 48 % preferred Brand A over Brand B and Brand C
A. What is the margin of error for the survey?
B. Give an interval that is likely to contain the exact percent of all people who prefer Brand A
c. In a survey of 1202 people, 11% said that they use the internet or e-mail more than 10 hours per week.
A. What is the margin of error for the survey?
B. How many people would need to be surveyed to reduce the margin of error to ±2%
d. A polling company conducts a poll for a U.S. presidential election. How many people did the company
survey if the margin of error is ±5%