Question

question
part 2 of 4
completed: 4 of 7 | my score: 4/7 pts (57.14%)
blocking refers to the idea that the variability in a variable can be reduced by segmenting the data by some other variable. the data in the accompanying table represent the recumbent length (in centimeters) of a sample of 10 males and 10 females who are 40 months of age. complete parts (a) through (d).
click the icon to view the data table.
(a) determine the standard deviation of recumbent length for all 20 observations.
6.08 cm (round to two decimal places as needed.)
(b) determine the standard deviation of recumbent length for the males.
□ cm (round to two decimal places as needed.)
more info
full data set
males
103.0 94.4
93.7 97.6
98.3 100.6
86.2 103.0
90.7 100.9
females
102.5 100.8
100.0 96.3
102.8 105.0
98.1 106.5
95.4 114.5

Explanation:

Step1: List male length data

Male data: $103.0, 94.4, 93.7, 97.6, 98.3, 100.6, 86.2, 103.0, 90.7, 100.9$

Step2: Calculate sample mean

Mean $\bar{x} = \frac{103.0+94.4+93.7+97.6+98.3+100.6+86.2+103.0+90.7+100.9}{10}$
$\bar{x} = \frac{968.4}{10} = 96.84$

Step3: Compute squared deviations

For each value $x_i$, calculate $(x_i-\bar{x})^2$:
$(103.0-96.84)^2=37.9456$, $(94.4-96.84)^2=5.9536$,
$(93.7-96.84)^2=9.8596$, $(97.6-96.84)^2=0.5776$,
$(98.3-96.84)^2=2.1316$, $(100.6-96.84)^2=14.1376$,
$(86.2-96.84)^2=113.2096$, $(103.0-96.84)^2=37.9456$,
$(90.7-96.84)^2=37.6996$, $(100.9-96.84)^2=16.4836$

Step4: Sum squared deviations

Sum $= 37.9456+5.9536+9.8596+0.5776+2.1316+14.1376+113.2096+37.9456+37.6996+16.4836 = 275.944$

Step5: Calculate sample standard deviation

Sample standard deviation $s = \sqrt{\frac{\sum(x_i-\bar{x})^2}{n-1}} = \sqrt{\frac{275.944}{10-1}}$
$s = \sqrt{\frac{275.944}{9}} \approx \sqrt{30.6604} \approx 5.54$

Answer:

5.54 cm