Answer:
a)Mean= 21.75, median 15.8 and standard deviation is 19.45
b)0.918
c)0.92
Step-by-step explanation:
a)Given this data in $, the mean is sum of data divided by number of samples
4.2 6.3 7.5 11.2 13.0 13.6 15.2 15.8 16.7 17.4 18.6 22.3 37.6 43.2 83.6
sum will be
[tex]4.2+ 6.3+ 7.5+ 11.2 +13.0+ 13.6+ 15.2+ 15.8+ 16.7+ 17.4+ 18.6+ 22.3+ 37.6+ 43.2+ 83.6=326.2[/tex]
Number of samples=15
Mean=326.2/15=21.75
Median is center value in the data set
4.2 6.3 7.5 11.2 13.0 13.6 15.2 15.8 16.7 17.4 18.6 22.3 37.6 43.2 83.6
Median=15.8
Standard deviation
4.2-21.75= -17.55 , -17.55² =308.00
6.3-21.75= -15.45, -15.45²= 238.70
7.5-21.75= -14.25, -14.25² = 203.06
11.2-21.75= -10.55, -10.55² = 111.30
13-21.75= -8.75, -8.75²= 76.56
13.6-21.75= -8.15, -8.15²= 66.42
15.2-21.75= -6.55, -6.55²= 42.90
15.8-21.75= -5.95, -5.95²= 35.40
16.7-21.75= -5.05, -5.05²= 25.50
17.4-21.75= -4.35, -4.35²= 18.92
18.6-21.75= -3.15, -3.15²= 9.92
22.3-21.75= 0.55, 0.55²=0.30
37.6-21.75=15.85. 15.85²=251.22
43.2-21.75=21.45, 21.45²=460.10
83.6-21.75=61.85, 61.85²=3825.42
mean of squared differences
308+238.70+203.06+111.30+76.56+66.42+42.90+35.40+25.50+18.92+9.92+0.30+251.22+460.10+3825.42=5673.72
Mean of squared differences=5673.72/15 =378.25------variance
Standard deviation is square-root of variance= √378.25=19.45
b) The formula for finding the coefficient of skewness using Person's method is;
Multiply the difference between mean and median by three then dividing the answer by the standard deviation
Sk₂=3(x-Md)/s
where Sk₂=skewness, x=mean, Md =median and s is standard deviation
Sk₂=3(21.75-15.8)/19.45 =0.918
c) using software method, use Excel
Answer=0.92
