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M116 – TI 83/84 CALCULATOR – CH 1
Section 1.2 – Random number generator
1) Select 3 students at random from your Statistics class.
a) There are 28 students in your class. Select 3 students at random.
Use the TI-83 calculator to generate 3 random integers from 1 to 28.
The instruction in the home screen of your calculator should read:
randInt(1,28,3)
Here are the steps to accomplish this:
Press MATH, arrow right to PRB, and select 5:randInt(
Type 1,28,3)
Notice: the “,” is the black key
Above the key for the number 7
Press ENTER
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M116 – TI 83/84 CALCULATOR – CH 2
Section 2.2 – Using the calculator to
Create a New List, Sort, and construct a Frequency Distribution
3) To get ready for this activity, create a new list labeled GLUCO
Here are the steps to accomplish this:
Press STAT
Select 1:Edit
Arrow right and up until the cursor is on the name of the last list of
your editor (the name has to be highlighted)
Arrow right and type the name of the new list: GLUCO
Press ENTER
Enter the data from problem 2 page 67. Press ENTER after each entry. All the numbers
should go into the same list.
4) Construct a frequency distribution of 6 classes for the GLUCO data.
a) Calculate the class width:
class.width 
l arg est.value  lowest.value
(rounded up)
number.of .classes
b) Use the smallest number as the lower limit of the first class. Obtain all other lower limits
by adding the class width. Then write the upper limits.
Classes
Frequency
c) In order to determine the frequencies we are going to SORT the list GLUCO, and then
explore the list to count how many values are in each of the classes.
To SORT the list press STAT, select 2:SortA(
Press 2nd STAT to select the list GLUCO
Press ENTER
Then, get into the editor by pressing STAT, 1:Edit and scroll down to determine the
frequencies.
Count how many numbers are in each class and record on the table from part b.
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d) Using your results from part (b), complete the following table:
CHAPTER 2
Class limits
Relative
frequency
Class
midpoint
Class
boundaries
Frequency
Cumulative
frequency
e) Sketch the corresponding histogram and label.
Use the same graph to sketch the corresponding frequency polygon for the data
Using words describe the coordinates of the points on the frequency polygon
(...................................................., ..........................................................)
f) Sketch the corresponding ogive –
Using words describe the coordinates of the points on the ogive
(...................................................., ..........................................................)
g) Sketch a Stem and Leaf plot for the GLUCO data (from #2 on page 67).
(Make sure the columns are aligned)
h) Sketch a Dot Plot for the GLUCO data. Dot plots are explained in problem #17 on pages 73
and 74 -
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M116 – TI 83/84 CALCULATOR – CH 2
Section 2.2 – Using the calculator to Sketch Histograms for Raw Data
5) Use the calculator to sketch a histogram for the data stored in GLUCO.
Here are the steps to accomplish this:
1st: Set up the histogram
Press 2nd Y= [STAT PLOT]
Select 1:Plot1… (or any other plot)
Turn the plot ON by pressing ENTER
Arrow down and to the right to select the histogram
Indicate GLUCO for the location of the data in Xlist
To select GLUCO press 2nd STAT[LIST], scroll down
and press ENTER to select
Indicate 1 for Freq
(Notice: Press ALPHA 1)
2nd: Set up the WINDOW. To sketch a histogram with a specific class width,
we need to set up the window values according to the specifications given
below.
You will need some numbers from the classes produced in the previous page
Press WINDOW
Use the following values:
Xmin = lower class limit of the first class
Xmax =lower class limit of the next class beyond the data
(Xmin + (number of classes)*(class width))
Xscl = class width
Ymin = -5
Ymax = a number larger than the largest frequency
(try any number, then adjust if necessary)
Yscl = 1
Yres = 1
Press GRAPH
3rd: Read the frequencies
Press TRACE and arrow to the right to read the classes and
frequencies.
Make sure the classes agree with the ones obtained in the previous page. Sketch the
histogram here.
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M116 – TI 83/84 CALCULATOR – CH 2
6) Use the calculator to sketch a histogram for the grouped data from part 4-d
(Use L1, L2)
Enter midpoints into L1 and frequencies into L2
In the STAT PLOT window, when you select the histogram, indicate L1 for XList
and L2 for Freq
If you still have the same WINDOW selections as indicated on the previous page,
press GRAPH and TRACE to check on the class limits and frequencies.
7) Explore the feature ZOOM 9:ZoomStat. Press TRACE, arrow to the right and observe
the frequencies. Are they the same as the ones obtained before?
What is the class width? What are the class limits of the first and second class?
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M116 – TI 83/84 CALCULATOR – CH 3
Sections 3.1-3.4 – Using the calculator to
Find the Mean, Median, Standard Deviation, and 5-number Summary
8) Use the data from problem 2, page 67, which you have stored into the list GLUCO, to
find the mean, standard deviation and the 5-number summary

Raw Data (list of all 70 numbers listed on page 67)
Instructions in the home screen should read 1-Var Stats GLUCO
Press STAT
Arrow to CALC
Select 1:1-Var Stats
Select the list GLUCO from the 2nd STAT (LIST) menu
Press ENTER

Grouped Data (use midpoints and frequencies. See page 4)
Instructions in the home screen should read: 1-Var Stats L1,Ll2
Enter midpoints into a list (L1),
Enter frequencies into another list (L2)
Press STAT
Arrow over to CALC
Press 1:1-Var Stats
Select L1, L2
Press ENTER

Observe the values obtained for the raw data and for the grouped data. Are they the
same? If not, why is that? Which answers are exact?
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M116 – TI 83/84 CALCULATOR – CH 3
Section 3.4 – Using the calculator to construct Box-and-Whisker Plots, and TRACE to
find the 5-number summary
9) Use the data from problem 2, page 67 (which is stored into the list GLUCO), to
construct a box plot
Here are the steps to accomplish this:
Press 2nd Y= (STAT PLOTS)
Turn one Plot ON, and make sure all others are OFF.
Arrow down and right to select the box plot that shows the outliers
Select GLUCO for Xlist (from the 2nd STAT[LIST] menu)
Select 1 for Freq
Press ZOOM 9 (this automatically opens an appropriate window)
Press TRACE and use the left-right arrows to obtain the 5-number
summary
_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_
10) Constructing the Box Plot and Histogram for the same data
Here are the steps to accomplish this:
Turn ON a second plot
Select a histogram for the data stored in list GLUCO
Press GRAPH
If necessary, press the WINDOW key and select a larger number for Y-max to provide
enough space to graph the histogram and the box-plot.
_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_____|_
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M116 – NOTES – CH 3
Section 3.2 - Chebyshev’s Theorem
For any set of data (either population or sample) and for any constant k greater than 1, the
proportion of the data that must lie within k standard deviations on either side of the mean is at
least 1-1/k^2
For any set of data
 At least 75% of the data fall win the interval from µ- 2σ to µ+ 2σ
(Within 2 standard deviations from the mean)
 At least 89% of the data fall win the interval from µ- 3σ to µ+ 3σ
(Within 3 standard deviations from the mean)
 At least 93.8% of the data fall win the interval from µ- 4σ to µ+ 4σ
(Within 4 standard deviations from the mean)
Empirical Rule and Range Rule of Thumb
Empirical Rule (section 6.1)
For a distribution that is symmetrical and bell-shaped (normal distribution)



About 68% of the data fall within the interval from µ- σ to µ+ σ
(Within 1 standard deviation of the mean)
About 95% of the data fall within the interval from µ- 2σ to µ+ 2σ
(Within 2 standard deviations of the mean)
About 99.7% of the data fall within the interval from µ- 3σ to µ+ 3σ
(Within 3 standard deviations of the mean)
Range rule of thumb (section 6.2)
The range rule of thumb is based on the principle that for many data sets (symmetrical, bell
shaped), the vast majority (such as 95%) of sample values lie within two standard deviations of
the mean.
To roughly estimate the standard deviation, use:
s ~ (highest value – lowest value)/4
To roughly estimate the minimum and maximum “usual” sample values, use:
Minimum “usual” value ~ mean – 2 * standard deviation
Maximum “usual” value ~ mean + 2 * standard deviation
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Example
a) Explore the SORTED data which is in the GLUCO list and determine the actual percentage
of values which lies
i) Within two standard deviations from the mean
ii) Within three standard deviations from the mean
iii) Within four standard deviations from the mean
b) What are these percentages suggesting about the shape of the GLUCO distribution?
c) What values of the GLUCO data are usual, which ones are unusual?
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M116 – NOTES
Choosing an appropriate number to describe the data
Measuring the center of a distribution

The mean cannot resist the influence of extreme observations. It is not a resistant measure of
the center

The median is a resistant measure of the center.

If the distribution is symmetric, the mean and median are the same.

If the distribution is close to symmetric, the mean and median are very close in values.

In a skewed distribution, the mean is farther out in the long tail than is the median
Measuring the spread of a distribution – Box Plots and the 5-number summary

The minimum and maximum values show the full spread of the data (but they may be outliers)

The interquartile range marks the spread of the middle half of the data.

In a symmetric distribution, the first and third quartiles are equally distant from the median

In most distributions that are skewed to the right, the third quartile will be farther above the
median than the first quartile

The standard deviation measures spread by looking at how far the observations are from their
mean
Choosing measures of center and spread

The five-number summary is usually better than the mean and standard deviation for
describing a skewed distribution or a distribution with strong outliers.

Use the mean and standard deviation only for reasonably symmetric distributions that are free
of outliers.
Example 1: Distributions of incomes are usually skewed to the right. Which measure of the center is
more appropriate? Why?

Reports about incomes and other strongly skewed distributions usually give the median rather
that the mean.
Example 2: The mean and median selling price of existing single-family homes sold in June 2002
were $163,900 and $210,900. Which of these numbers is the mean and which is the median? Explain
how you know.
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