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?