Question

1. A researcher wants to determine the average wage of American steel workers. A sample of 12 workers was selected randomly and indicated the following wages:

$20, $14, $10, $11, $12, $40, $30, $21, $22, $20, $20, $20

Find the mean and the standard deviation.

mean=$20; sd=$8.45

mean=$20; sd=$71.45

mean=$20; sd=$65.5

mean=$20; sd=$8.09

2. A researcher wants to determine the average wage of American steel workers. A sample of 12 workers was selected randomly and indicated the following wages:

$20, $14, $10, $11, $12, $40, $30, $21, $22, $20, $20, $20

Find the median, Q1 and Q3.

median=$20; Q1=$12; Q3=$21

median=$20; Q1=$13; Q3=$22

median=$20; Q1=$13; Q3=$21.5

median=$20; Q1=$14; Q3=$22

Answer 1

Solution:-

1.)

given sample: $20, $14, $10, $11, $12, $40, $30, $21, $22, $20, $20, $20

Mean=(20+14+10+11+12+40+30+21+22+20+20+20)/12=$20

Standard Deviation=$8.45 (use:'=STDEV.S()' in excel)

ans: mean=$20; sd=$8.45

2.)

Given Sample: $20, $14, $10, $11, $12, $40, $30, $21, $22, $20, $20, $20

in Ascending order: 10,11,12,14,20,20,20,20,21,22,30,40

Median=(6th+7th) terms/2

=(20+20)/2

=20

Lower Half of the data:10,11,12,14,20,20

Q1(lower Quartile)=median of lower half of the data

Q1=(12+14)/2=$13

upper Half of the data: 20,20,21,22,30,40

Q3(upper quartile)=median of lower half of the data

Q3=(21+22)/2=21.5

Ans:-median=$20; Q1=$13; Q3=$21.5