1. Chapter 3: Transformations of Graphs and Data Lesson 6: Scale Changes of Data Mrs. Parziale

2. Example 1: Consider the following set of data: 4, 2, 5, 9, -1, 6, 3, 2 (a) Calculate the following: Mean = _____ Median = ____ Mode = ____ Range = ____ Std. Dev = ___ Variance = ____

4. 4, 2, 5, 9, -1, 6, 3, 2 (b) Multiply every term in the set by (a) where a = 3. List the new elements: ____ ____ ____ ____ Calculate the following: Mean = _____ Median = ____ Mode = ____ Range = ____ Std. Dev = ___ Variance = ____

5. 4, 2, 5, 9, -1, 6, 3, 2 (b) Multiply every term in the set by (a) where a = -3. List the new elements: ____ ____ ____ ____ Calculate the following: Mean = _____ Median = ____ Mode = ____ Range = ____ Std. Dev = ___ Variance = ____

6. What Happens When you multiply a set of data by some constant “a”, what happens to each of the following? Mean = _____ Median = ____ Mode = ____ Range = ____ Std. Dev = ___ Variance = ____ Multiplied by “a” Multiplied by |a| Multiplied by a 2

7. Example 2: The teachers in a school have a mean salary of $30,000 with a standard deviation of $4,000. If each teacher is given a 5% raise, what will be their new mean salary and the new standard deviation?

8. Example 3: To give an approximate conversion from miles to kilometers you can multiply the number of miles by 1.61. Suppose data are collected about the number of miles that cars can go on a tank of gas. What will be the effect of changing from miles to kilometers on: (a) the median of the data? ________________________ (b) the variance of the data? _______________________ (c) the standard deviation of the data? ________________

9. Closure Given a set of data. If you multiply each data item by 5, – how does this effect the measures of center? – how does this effect the measures of spread? range Standard deviation Variation How are these values changed if the data is multiplied by -5?