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Chapter 3: Transformations of Graphs and Data
Lesson 3: Translations of Data
Mrs. Parziale
Example 1:
Suppose a small class yields the following set of test scores:87, 86, 85, 81, 78, 75, 75, 73, 70, 68, 67, 63.
a) Find the measures of central tendency: mean _____ median: _____ mode: _____
b) Give the five-number summary:_____, _____, ______, ______, ______
c) Find the measures of spread:standard deviation _____ variance ______
range _____ IQR _____
Scale the Test
Now, suppose the teacher scales the test, adding 12 points to each score. Recalculate the measurements. Which change, and how?
New Scores:99, 98, 97, 93, 90, 87, 87, 85,
82, 80, 79, 75
Measurement
Original New Value
Change
Mean 75.667
Median 75
Mode 75
Min 63
Max 87
Q1 69
Q3 83
Std Dev 7.92
Variance 62.79
Range 24
IQR 14
Theorems
• Theorem: Adding (h) to each number in a data set adds h to each of the mean, median, and mode.
• Theorem: Adding (h) to each number in a data set does not change the range, interquartile range, variance, or standard deviation.
• The second theorem is true because these are all measures of spread, and the spread of the data does not change if each point is translated h points up or down.
• Because these measures of spread do not change under a translation, they are called invariant under a translation. INVARIANT means unchanging.
Example 2:
Evaluate the following for the set
(summation, add 6) (add 6 to each term in the summation)
1 2 3 44 7 6 9p p p p
4
1
6ii
p
4
1
( 6)ii
p
How can you do this on your TI 83?
Example 3: Reducing an entire list of data on the TI-83.
• Find the line of best fit for the dataset to the left: ______________________
• Now, find the line of best fit where x = # of years after 1900. ___________________
• How did you do it? Can you do it without changing the lists in your calculator?
L1 L21960 45
1963 43
1965 42
1969 40.5
1972 39
Check Your Equations
Check this in your calculator to verify your answer.
L1 L21960 45
1963 43
1965 42
1969 40.5
1972 39
Enter the two equations into your TI83
.48 985.83
.48 73.83
y x
y x
Closure
• What kind of effect does adding a value of h to the numbers in a dataset have on the measures of central tendency and measures of spread?
• How can you use your calculator to make a change to an entire list of data without changing the list in the calculator?
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