For each of the following data sets, compute xbar, s2, and s. If appropriate, specify the units in which your answers are expressed.

a.4, 6, 6, 5, 6, 7

b.- \(1, \)4, - \(3, \)0, - \(3, - \)6

c.3/5 %, 4/5 %, 2/5 %, 1/5 %, 1/16 %

d.Calculate the range of each data set in parts a–c.

Short Answer

Expert verified

a. mean= 5.66, s2 = 1.066, s = 1.03

b. mean = -$1.5, s2 = 11.95, s = $3.45c

c. mean = 0.4125%, s2 = 0.088, s = 0.29%

d. a = 3, b = $10, c = 0.7375%

Step by step solution

01

Computing xbar, s2, and s for a

χn=4+6+6+5+6+76=346=5.66

s2=χ2n1=45.662+65.662+65.662+55.662+65.662+75.66261=2.7556+0.1156+0.1156+0.4356+0.1156+1.79565=5.33365

=1.066

s=s2=1.066=1.03

Therefore, mean = 5.66, s2 = 1.066, s = 1.03

02

Calculating xbar, s2, and s for b

χn=1+4+(3)+0+(3)+(6)6=96=1.5

s2=χ2n1=11.52+41.52+31.52+01.52+31.52+61.5261=0.25+30.25+3+3+3+20.255=59.755=11.95

s=s2=11.95=3.45

Therefore, mean = -$1.5, s2 = 11.95, s = $3.45

03

Estimating xbar, s2, and s for c

χn=0.6+0.8+0.4+0.2+0.06255=2.06255=0.4125%

s2=χ2n1=0.60.41252+0.80.41252+0.40.41252+0.20.41252+0.06250.4125251=0.035+0.15+0.00015+0.045+0.12254=0.354

=0.088

s=s2=0.088=0.29%

Therefore, mean = 0.4125%, s2 = 0.088, s = 0.29%

s2=χ2n1=0.60.41252+0.80.41252+0.40.41252+0.20.41252+0.06250.4125251=0.035+0.15+0.00015+0.045+0.12254=0.354

04

Finding the Range

Range = Max – Min

  1. 4, 6, 6, 5, 6, 7

Range=MaxMin=74=3

b. - $1, $4, - $3, $0, - $3, - $6



Range=MaxMin=46=$10


c. 3/5 %, 4/5 %, 2/5 %, 1/5 %, 1/16 %

Range=MaxMin=0.80.0625=0.7375%

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