Consider the following data from a random sample: 23 12 26 14 20 25 14 11 21 14 25 21 22 21 8 19 17 22 17 16
a.) Construct a stemandleaf plot and specify the fivenumber index (min, Q1, Q2, Q3, & max)
b.) Compute the mean and the standard deviation
c.) Find a 95% confidence interval for the population mean.
Solution : Given data 23,12,26,14,20,25,14,11,21,14,25,21,22,21,8,19,17,22,17,16
=> Ascending ordering as 8,11,12,14,14,14,16,17,17,19,20,21,21,21,22,22,23,25,25,26
a.) Stem and leaf plot :
stem  leaf

0  8
1  1 2 4 4 4 6 7 9
2  0 1 1 1 2 2 3 5 5 6
Five number index is :
Minimum = 8
Quartile1 Q1 = 14
median Q2 = 19.5
Quartile1 Q3 = 22
Maximum = 26
b.) mean = sum of the terms/number of the terms
= (8 + 11 + 12 + 14 + 14 +....+ 26 )/20
= 368/20
x = 18.4
Standard deviation ? = 5.0617
c.) For 95% confidence interval , Z = 1.96
=> The 95% confidence interval for the population mean is x
+/ Z*?/sqrt(n)
=> 18.4 +/ 1.96*5.0617/sqrt(20)
=> (16.1816 , 20.6184)
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