Download With our data for Example 3

Examples from Blu4, Chapter 3
Background skills – putting data into a “list” on the TI-84 and related activities, such as clearing a list, are
assumed. If you need to know about them, refer to this handout: . ..\TI-84_General\TI-84_Lists.pdf
Example 3-1 – Find the mean
Put the data into a list. We used
list L1.
Press the STAT key.
→ to the CALC submenu.
1:1-Var Stats
ENTER.
The mean is the value shown at
the 𝑥̅ = line. We round off the
mean to one more decimal place
than what is shown in the data.
Our final answer is 𝑥̅ = 30.7.
We say “𝑥̅ = 30.7”, not just the
number “30.7” by itself. The
other values on this screen will
be discussed in other examples.
Example 3-2 – Find the mean – using a list other than list L1
Put the data into a list. We’re
going to use List L2.
STAT, →, 1:1-Var Stats again,
but don’t press ENTER yet!
The 1-Var Stats command uses list L1 by default. We tell it to use
List L2: 2ND STAT 2:L2.
Then ENTER. We answer with
“𝑥̅ = 5.77”, rounding to one
place more than the data.
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Example 3-2 redone with { list } rather than a stored list
2ND STAT ← 3:mean(
Put the list inside squiggly braces. 2ND ( for the starting “{“
Then the values separated by commas 2ND ) for the ending “}”
Close the right parenthesis ) Aand press ENTER.
Example 3-3 – The mean of a frequency distribution
Put the class midpoints into one
list (we used L1, the values are
column “C” in the book’s byhand calculation)) and the
corresponding frequencies into
another list (we used L2, the
values are in column “B” in the
book’s by-hand calculation.)
STAT → 1:1-Var Stats as usual,
but next comes something
different:
2ND STAT 1:L1
, the comma key
2ND STAT 2:L2
Quick typing check: the two lists
must have the same number of
elements; they end at the same
line in the lists screen.
This means “List L1 contains the
values and List L2 contains the
frequencies”. Press ENTER
Results:
𝑥̅ = 24.5 (we would have
rounded to one decimal place
anyhow).
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Examples 3-4, 3-5, 3-6, 3-7, and 3-8 – Find the median.
We put the data for all five of
these problems into lists L1
through L5.
The 1-Var Stats command gives
We do 1-Var Stats for each of the us more information than fits on
five lists: STAT → 1:1-Var Stats
a screen. Observe the down
arrow at the bottom of the first
2ND STAT #:L#.
page of data.
You must scroll down to get to
the median. See on the line that
says “Med=”. This is Example 34.
Here are the second page results
with the median for Example 35.
And Example 3-7
And Example 3-8
And Example 3-6.
Examples 3-9, 10, 11, 12, 13 – Find the Mode
The TI-84 doesn’t compute Mode for us.
Example 3-14 – Find both the Mean, Median, and Mode
The 1-Var Stats results give the Mean and Median (scroll to the second screen of results for the Median),
so the list only needs to be typed once, the 1-Var Stats command only needs to be issued once, and
many questions are answered. The Mode must be done manually.
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Example 3-15, 16 – Find the Midrange
Put the data into lists. We used
list L1 for Example 3-15 and list
L2 for Example 3-16.
Do 1-Var Stats for each list.
Scroll to the second screen.
Here are results for Ex. 3-15
Here are 1-Var Stats for Example
3-16.
The 1-Var Stats does not
compute midrange for us. But
we can finish by hand:
Example 3-15:
Example 3-16:
Midrange =
Midrange
(1+8)
=
2
= 4.5
Midrange =
(1+16)
2
= 8.5
(𝑚𝑖𝑛𝑋+𝑚𝑎𝑥𝑋)
2
Example 3-17 – Weighted Average
This works exactly the same as finding the mean of a frequency distribution. The “weight” of each value
acts like the “frequency” did in the frequency distribution.
We put the grade points (A = 4, B
= 3, C = 2, D = 1, F = 0) into list L1
and the weights (the
corresponding credit value of
each course) in list L2.
Then we do 1-Var Stats L1,L2
The weighted mean is in the 𝑥̅ .
The GPA is rounded to 2.67 or
2.7.
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Examples 3-18, 19, 20, 21, 22 – Variance and Standard Deviation
These examples all use the lifetime of two different brands of paints and make comparisons..
We use list L1 for the sample of
lifetimes for Brand A and list L2 fo
rthe sample of lifetimes for
Brand B.
Here are results for Brand A
Here are results for Brand B
Remarks
Both Brands have mean lifetime
𝑥̅ = 35 but the underlying data
are greatly different between
the two brands.
𝑆𝑥=sample standard deviation
(the (𝑛 + 1) denominator) and
𝜎𝑥=population standard
deviation (the 𝑛 denominator).
If you need either of the
variances, take the standard
deviation and square it.
Another way to get the variance
Suppose we want a super-precise value for the sample variance of Brand B and we don’t want to retype
7.071067812. With the “1-Var Stats L2“ results fresh in the calculator’s memory, do the following:
VARS
5:Statistics
3:Sx X2 ENTER . The sample
variance, (Sx)2 in calculator
language and 𝑠 2 in proper
statistics language, is 50.
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Example 3-23 – Sample variance and Sample standard deviation
The first bunch of examples on variance and standard deviation introduced four ideas all at once:
With the 𝑛 in the denominator of the formula
Population variance
Population standard deviation
with the (𝑛 − 1) in the denominator of the formula
Sample variance
Sample standard deviation
But usually it’s going to be the sample standard deviation that we’re interested in.
With our data for Example 3-23 in List L1,
STAT → 1:1-Var Stats ENTER
It gives us BOTH.
We read the problem carefully
and see that the sample
variance and sample standard
deviation are requested.
Sample Standard Deviation
Is calculator’s Sx, properly
named 𝑠 or 𝑠𝑥 .
To get the variance, either retype
and square the value, with more
decimal places for more
accuracy.
Or use the VARS 5:Statistics 3:Sx
and square that value.
Population standard deviation is
the calculator’s σx, properly
called 𝜎 or 𝜎𝑥 .
Final answers:
The sample variance is 𝑠 2 =
1.28 and the sample standard
deviation is 𝑠 = 1.13.
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Example 3-24 – Variance and Standard Deviation of a frequency distribution
When they don’t explicitly say “find the sample standard deviation”, they mean the sample standard
deviation. Don’t use the population standard deviation unless they say they want that one in particular.
Recall the earlier example when we used the 1-Var Stats L1,L2 to find the mean of a frequency
distribution. The same procedure does all the other statistics for a frequency distribution, too.
Put the data values into list L1
(the Midpoint column in their byhand example) and the
frequencies into list L2.
STAT → 1:1-Var Stats
2ND STAT 1:L1 , (comma)
2ND STAT 2:L2 ENTER
Since it’s implied that it’s the
sample standard deviation they
want, we use the
Sx=8.287593772 and square it
(VARS 5:Statistics 3:Sx X2
ENTER) to get 68.68421053.
Our answers are:
The (sample) standard deviation
is 𝑠 = 8.3 and the (sample)
variance is 𝑠 2 = 68.7.
Examples 3-25, 26 – The coefficient of variation
This is a plain arithmetic calculation; there is no built-in TI-84 variable to give this value.
Examples 3-27, 28 – Chebyshev’s Theorem
This involves algebra and arithmetic; there is no built-in TI-84 way to solve these problems.
Examples 3-29, 30 – Standard scores (z scores)
This is a plain arithmetic calculation; there is no built-in TI-84 variable to give this value.
Examples 3-31, 32, 33, 34, 35 – Percentiles
There is no built-in TI-84 method for doing these problems.
Example 3-36 – Quartiles
Put the data into a TI-84 list and
use 1-Var Stats to find
𝑄1 , 𝑄2 , 𝑄3 .
(You need to scroll onto the
second screen of 1-Var Stats
results.)
Answers:
𝑄1 the first quartile, is 9.
𝑄2 is the median, which is 14.
𝑄3 is the third quartile, which is
20.
Example 3-37 – Outliers
There is no direct TI-84 way to find outliers. But you can use the 1-Var Stats to find 𝑄1 and 𝑄3 , and
from there the Interquartile Range and the low and high values of the interval for non-outliers is easily
found using arithmetic.
Examples 3-38, 39 – The Five-Number Summary and Boxplots
See separate document: Boxplot.pdf.
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