Questions: Module 1.4 Homework Question 12, 3.2.42 Part 1 of 4 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) (a) Determine the standard deviation of recumbent length for all 20 observations. Males Females --- --- 1030 94.4 1029 1008 940 976 1004 963 98.7 1006 1028 1050 862 1030 981 1065 907 1009 954 1145

Module 1.4 Homework
Question 12, 3.2.42
Part 1 of 4
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)

(a) Determine the standard deviation of recumbent length for all 20 observations.

Males Females
--- ---
1030 94.4 1029 1008
940 976 1004 963
98.7 1006 1028 1050
862 1030 981 1065
907 1009 954 1145

Transcript text: Module 1.4 Homework Question 12, 3.2.42 Part 1 of 4 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) (a) Determine the standard deviation of recumbent length for all 20 observations. \begin{tabular}{|c|c|c|c|c|} \hline & & \multicolumn{3}{|r|}{ Full data set 0} \\ \hline \multicolumn{2}{|l|}{ Males } & \multicolumn{2}{|l|}{ Females } & \\ \hline 1030 & 94.4 & 1029 & 1008 & \\ \hline 940 & 976 & 1004 & 963 & \\ \hline 98.7 & 1006 & 1028 & 1050 & \\ \hline 862 & 1030 & 981 & 1065 & \\ \hline 907 & 1009 & 954 & 1145 & \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Calculate the Mean (\(\mu\))

To find the mean (\(\mu\)) of the dataset, sum all the observations and divide by the total number of observations (\(N\)). \[\mu = \frac{\sum x_i}{N} = \frac{18180.1}{20} = 909.005\]

Step 2: Calculate Squared Differences from the Mean

For each observation \(x_i\), calculate the squared difference from the mean \((x_i - \mu)^2\).

Step 3: Sum All Squared Differences

The total squared variance is the sum of all squared differences: \[\sum (x_i - \mu)^2 = 1533938.249\]

Step 4: Calculate Variance

The variance of the dataset is calculated by dividing the total squared variance by \(N\): \[\sigma^2 = \frac{\sum (x_i - \mu)^2}{N} = 76696.912\]

Step 5: Calculate Standard Deviation

The standard deviation is the square root of the variance: \[\sigma = \sqrt{\sigma^2} = 276.94\]