Question

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 stem-and-leaf plot and specify the five-number index (min, Q1, Q2, Q3, & max)

b.) Compute the mean and the standard deviation

c.) Find a 95% confidence interval for the population mean.

Answer 1

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)