Question

The data set below contains penetration values (the percentage of a country's population who are users) for a popular website in 22 of the world's largest economies. Complete parts (a) through (d) below. 42 39 27 44 42 28 516 24 51 33 9 6 80 23 34 58 42 19 57 51 57 OB. There is no mode for this data set. b. Calculate the variance, standard deviation, range, coefficient of variation, and Z scores. Are there any outliers? Explain. The variance is 352.54. (Round to two decimal places as needed.) The standard deviation is 18.78 . (Round to two decimal places as needed.) The range is 74. (Round to two decimal places as needed.) The coefficient of variation is 50.19 %. (Round to two decimal places as needed.) Compute the Z scores for the first eight values. Data (X) Z Score (Round to two decimal places as needed.)

Answer 1

The dataset given below are: 42,39,27,44,24,33,9,23,34,58,42,42,28,51,6,51,6,80,19,57,51,57

From the dataset, it is clear that dataset has bimodel because the data poinnt 42 & 51 both has maximum frequency which is equal to 3.

Given thaty =42.39,234424,33,9, 23 3458 42 42, 2951 6,S,6 89 19, S34, S,57 823 - 37.41 22 22 Vananeea L(Xi-X -r42-39.4 +3 9-27. -+ ls4-37.41) 22 2 X21.08+2.53 + +383.80 22 구403.318 X 213,79 tandard deviahon Vvarane 213.79 142 Ranea mason obs min o bs 80-6=74 Coethrrent df variatons 14.62 -xloo 37.41 39.08 X

40 20 08 09

It is clear from the above boxplot, all the data points lie inside the boxplot. So, there is no outlier in the data.

Z-Score=(X-mean(X))/Sd(X)

i.e. for X=42, Z-score=(42-37.41)/14.62=0.31

Similary, when you will calculate Z-score for 29,27,44,24,33,9,23, you will get -0.58, -0.71, 0.45, -0.92, -0.30, -1.94, -0.99 respectively.

Note: In this problem, you have mentioned that the variance of the dataset is 352.54. I think you have taken (N-1=21) in the denominator which is wrong. Always divide by N in the denominator for calculating variance.