Question

can someone please help solve this problems. I don't know how to find the mean and standard deviation, and the outliers in the data. Thank You !

2. (12 pts] During his 20 seasons in the National Hockey League, Wayne Gretzky scored 50% more points than anyone who ever played professional hockey. He accomplished this amazing feat while playing in 280 fewer games than Gordie Howe, the previous record holder. Here are the number of games Gretzky played during each season 45 48 70 70 73 74 74 78 78 79 79 80 80 80 80 80 80 81 82 82 a. Find the mean and standard deviation for the data above. b. Find the five number summary c. Are there any outliers in the data? Show work and identity which value(s) if any are outliers. d. Construct a boxplot for the data e. Describe the shape, center, spread, and any unusual features in the data

Answer 1

0.2) a Mean of Total sum all the observations Total number of observations Mean 1493 20 74.65 0) standard deviation I Ž (x; -3)? m-1 i-T where Total no. N o. of 20 - 2° (xi-74-05) 19 ST Observations Ty mean obtains - Standard deviation 20. 302 xit refers to the ith observation = You You can also use Ms Excel for finding standard deviation Enter all the data set, the enter' = STDEV.S (array) in array' select all the cells in which date set is entered] bo) 5 number summary Minimum = 45 First auartile (a)= 73.75 Median (0)= 79 third Quaestile (Q3)= 80 Maximum 82 aiguse excel For fincing dig dion = QUARTILE (assay, 1) function For finding Median or da q use ex use excel function = MEDIAN (array) For finding Q3, use excel function = QUARTILE Carray, 3)

Lower outlier = c.) Yes outliers are present. [198=23-0 present. [igR=43-2, -80 -73.75= 6.25) (-5. IQR) = 73.75 - (1-5% (-25) 43 + (1-5 · IQR) - 80 + (1-5 X6-25) 64-375 Lower outlier Higher outlier Higher outlier 89.375 In the 9 given data set, 2 number :- 45 and 48 are less than 64-375 Clower outlico). This indicates that these numbers are the outlier. d.) Box plot 92 Cor Median) Qi Q3 outliers o ! 4,4.5X190) 9 +(-5XIQR) 40 45 50 55 60 65 70 75 so 85 go e. Shape heft- skewed Center - Mean = 74-65 and Median = 79 by lar Cinter cuartile Range) Spread Spread is represented 1QR = 92-Q, 80 73.75 = 6.25 Unusual features s 2 cuthiers in data set - 45 and 48
The mean and the standard deviation is calculated using the formula mentioned. We use MS Excel functions which have been mentioned to find the 5 number summary.