Question

Chapter 03, Testbank, Question 079-090 The following data represent the ages of 15 people buying lift tickets at a ski area 15 25 26 17 38 16 70 43 30 24 28 40 20 35 What is the mean of these data, rounded to two decimal places? What is the median of these data? What is the range of these data? What is the variance of these data, rounded to two decimal places? What is the standard deviation of these data, rounded to two decimal places? What is the value of the first quartile? What is the value of the third quartile? What is the value of the interquartile range? What is the value of the lower inner fence? What is the value of the upper inner fence? Are there any outliers in this data set? Click if you would like to Show Work for this question: Open Show Work 31

Answer 1

Given Data 15, 25, 26, 17, 38, 16, 70, 43, 30, 24, 28, 40, 20, 35, 31 Sample Mean X(x) 15 +25+ ...+31 458 15 30.533333 30.533 15 Mean: 30.533 Our sorted data is: 15, 16, 17, 20, 24, 25, 26, 28, 30, 31, 35, 38, 40, 43, 70 Since our data has 15 (odd) number of entries Median sth entry 28 Median 28 Range is the difference between largest and the smallest values of data. Range max-min = (70)-(15) = 55 Range 55 -3 15 25 26 17 15.533333 -5.533333 -4.533333 13.533333 241.284444 30.617778 20.551111 183.151111

38 16 70 43 30 24 28 40 20 35 31 1.4666b67 14.533333 211.217778 1557.617778 155.417778 0.284444 42.684444 6.417778 89.617778 110.951111 19.951111 0.217778 Σ (zi-z)2-2725.733333 39.466667 12.466667 0.533333 6.533333 -2.533333 9.466667 10.533333 4.466667 0.466667 458 15-30533333 Sample Variance s2- (15 - 30.533333)(25 30.533333)2+...+ (31 - 30.533333)2 15 1 (-15.533333) (-5.533333)2(0.466667) 14 2725.733333 14 194.695 Alternatively, we can use: s2 T2 = ĩ, 16710-20 ) 194.695238 ะ 194.695 14(16710 - 209764 Variance: 194.695 Sample Standard Deviation-s- 194.69513.953324 13.953 v 82 = 13.953324

Standard Deviation: 13.953 Our sorted data : 15, 16, 17, 20, 24, 25, 26, 28, 30, 31, 35, 38, 40, 43, 70) First Quartile is median of first half of data, .e. first 7 terms 15, 16, 17, 20, 24, 25, 26 ) Clearly the First quartile or median of this first half of data is 01 20 Third Quartile is median of second half of data, i.e. last 7 terms: 30, 31, 35, 38, 40, 43, 70) Clearly the Third quartile or median of this second half of data is 38 And Q2 is median of complete data, 2 28 The five number summmary is: Interquartile range is IQR- Qs-Q 18 IQR= 18 Lower fence for outlier Q1 1.5(Q3 Q1)7 Upper fence for outlier-Q1.5 (Qs- Q) 65 Outliers are the points either below lower limit or above upper limits. Outliers are: 70 eee. Thank you Av