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

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, 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 = ____

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 = ____

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

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?

Example 3: To give an approximate conversion from miles to kilometers you can multiply the number of miles by 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? ________________

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?