Chapter 6 Review Key

MAT 043 Chapter 6 Review 1. The data below represents the 2019 top ten Billionaires according to Forbes magazine. Billionaire Net Worth (billions of dollars) Steve Ballmer 52 Sergey Brin 54 Warren Buffett 81 Jim Walton 52 Larry Ellison 65 Larry Page 56 Bill Gates 106 Michael Bloomberg 53 Jeff Bezos 114 Mark Zuckerberg 70 n = 10 Use the data set above to find the following: a. Find the mean x = 703 10 = 70.3billion dollars b. Find the mode Mode = 52 billion dollars c. Find the median Data in order: 52, 52, 53, 54, 56, 65, 70, 81, 106, 114 Median = 60.5 billion dollars d. Find the range Range = highest − lowest = 114 − 52 = 62 billion dollars e. Determine the percentile ranking for the net worth of $54 billion 4 10 × 100 = 40% , so 40 th percentile f. Calculate the five-number summary for the data and then create a box and whisker plot to model the data Data in order: {52, 52, 53 Q 1 , 54, 56} 60.5 median {65, 70, 81 Q 3 , 106, 114} so, L=52, Q 1 =53, M=60.5, Q 3 =81, H=114 Indicate the five-number summary: {52, 53, 60.5, 81, 114}

Construct a box and whisker plot to model the data above: g. Characterize the data above: Right Skewed h. Use the five-number summary or the box and whisker plot to answer the following: a) What percent of the men are worth more than $53 billion? 75% b) What percent of the men are worth less than $60.5 billion? 50% c) What earning range did the middle 50% of the men earn? $53 billion to $81 billion i. Calculate the standard deviation for the net worth of the billionaires Mean: Use the table below to calculate the standard deviation: (Round to the nearest whole number) n = 10 x = 70.3 Data x − x ( x − x ) 2 52 52 − 70.3 =− 18.3 ( − 18.3 ) 2 = 334.89 54 54 − 70.3 =− 16.3 ( − 16.3 ) 2 = 265.69 81 81 − 70.3 = 10.7 ( 10.7 ) 2 = 114.49 52 52 − 70.3 =− 18.3 ( − 18.3 ) 2 = 334.89 65 65 − 70.3 =− 5.3 ( − 5.3 ) 2 = 28.09 56 56 − 70.3 =− 14.3 ( − 14.3 ) 2 = 204.49 106 106 − 70.3 = 35.7 ( 35.7 ) 2 = 1274.49 53 53 − 70.3 =− 17.3 ( − 17.3 ) 2 = 299.29 114 114 − 70.3 = 43.7 ( 43.7 ) 2 = 1909.69 70 70 − 70.3 =− 0.3 ( − 0.3 ) 2 = 0.09 Total 0 4766.2 S = √ ∑ ( x − x ) 2 n − 1 = √ 4766.2 9 ≈ 23.01 Standard Deviation: $23.01 billion