Question

PLEASE ANSWER!

173   156   148   164   153   126   178   168   173   170   120

a) Calculate the mean, median and mode.  

b) How would you describe this distribution in terms of skewness?  

c) How did you use these numbers to figure out the skewness?

Answer 1

120
126
148
153
156
164
168
170
173
173
178

Above is the sorted data , in increasing order .

Total number of data is 11 , middle most data is 6th term , that is 164 so median is 164 .

173 occur 2 times in the data so it is the mode .

Therefore mean =

(120+126+148+153+156+164+168+170+173+173+178)/11

= 157.18

Now Standard deviation

Sd= root[summation(X-mean)²/n]

so sd = (3719.64/11)^1/2 = 18.388

B)Now , skewness .

So Karl Pearson coefficient of skewness is

Sk = (mean-mode)/sd

= (157.18-173)/18.388

= -0.8630

The skewness is comming to be -0.8630 .

A negative skew refers to flatter or longer tails to the left of the distribution .

C) according to Karl Pearson skewness is given by

Sk= Mean - mode / sd

Or sk = 3(mean-median)/sd

When ever mean<median or mean < mode we deal with negative skewness .

Cnt X X-u (X - u)2 n 1 120 120 - 157.18 = -37.18 (-37.18)2 = 1382.49 2 126 126 - 157.18 = -31.18 (-31.18)2 = 972.31 3 148 148 - 157.18 = -9.18 (-9.18)2 = 84.31 4 153 153 - 157.18 = -4.18 (-4.18)2 = 17.49 5 156 156 - 157.18 = -1.18 (-1.18)2 = 1.40 6 164 164 - 157.18 = 6.82 (6.82)2 = 46.49 7 168 168 - 157.18 = 10.82 (10.82)2 = 117.03 8 170 170 - 157.18 = 12.82 (12.82)2 = 164.31 9 173 173 - 157.18 = 15.82 (15.82)2 = 250.21 10 173 173 - 157.18 = 15.82 (15.82)2 = 250.21 11 178 178 - 157.18 = 20.82 (20.82)2 = 433.40 n = 11 Sum = 1729 E (X - u)2 = 3719.64