Question

The following data represent the dividend yields​ (in percent) of a random sample of 28 publicly traded stocks. (a) Compute the​ five-number summary. ​(b) Draw a boxplot of the data. (c) Determine the shape of the distribution from the boxplot.

1.25	0.49	1.66	2.7	0.42	2.75	0.69
0	0.28	2.79	0	1.55	2.84	0.48
0.48	3.58	1.09	0.92	2.57	3.23	0
0.12	0	2.44	2.19	2.99	1.87	0.51

Answer 1

in ascendin 1.25 Ans(a). Five number theory include minimun value, maximum value, lower and uper quartile, and median. Let ql be lower quartile, M be median and q3 be upper quartile, 0.49 1.66 Calculation, Ans(b) q1 (n+1)/4)th value-> (28+1)/4-> 7.25th value-> 7th value + .25 *( 8th value-7th value) q1 = .42+0.25"(.48-42) => .435 0.42 0.12 Box Plot 2.75 0.28 10 0.69 0.42 M ((n+1)/2)th value 14.5 th value >average of 14th and 15th value (1.09+1.25)/2 1.17 0.48 3.5 0.28 0.48 2.79 0.49 q3 (3*(n+1)/4) th value 21.75th value21th value+.75( 22th value 21th value) q3 2.57+.75*(2.7-2.57)-2.6675 0.51 1.55 0.69 2.84 0.92 Minimum value=0 1.5 17 0.48 1.09 17 Maximum value 3.58 0.48 1.25 19 3.58 1.55 0.5 To check outlier 20 1.09 1.66 lower outlier ql-1.5* IQR->(435-1.5 (2.6675 435)) -2.91375 upper outlier-q3+1.5*IQR-> (2.6675+1.5"( 2.6675-.435))-> б.01625 0.92 1.8 2.5 2.19 3.23 2.44 Ans c. The shape of the distribution is positive skewed because value of median(1.17) is less than mean(1.42) 2.57 0.12 2.7 26 2.75 2.44 2.79 28 2.19 2.84 29 2.99 2.99 3.23 0.51 3.58 vate Sheet1 9:17 PM