Chapter 3: Transformations of Graphs and Data Lesson 3: Translations of Data Mrs. Parziale.

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Presentation transcript:

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 Measure ment OriginalNew Value Change Mean Median75 Mode75 Min63 Max87 Q169 Q383 Std Dev7.92 Variance62.79 Range24 IQR14

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) 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 ___________________ How did you do it? Can you do it without changing the lists in your calculator? L1L1 L2L

Check Your Equations Check this in your calculator to verify your answer. L1L1 L2L Enter the two equations into your TI83

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?