Question

for the data shown, answer the questions. round to 2 decimal places.

x
28.8
3.6
21.2
21.8
29.8

compute the sample mean:

compute the median:

compute the sample standard deviation:

Explanation:

Step1: Compute Sample Mean

Sum the data: \(28.8 + 3.6 + 21.2 + 21.8 + 29.8 = 105.2\).
Divide by \(n = 5\): \(\frac{105.2}{5} = 21.04\).

Step2: Compute Median

Sort data: \(3.6, 21.2, 21.8, 28.8, 29.8\).
Middle term (3rd) is \(21.8\).

Step3: Compute Sample Standard Deviation

1. Find deviations from mean:

\(28.8 - 21.04 = 7.76\), \(3.6 - 21.04 = -17.44\), \(21.2 - 21.04 = 0.16\), \(21.8 - 21.04 = 0.76\), \(29.8 - 21.04 = 8.76\).

1. Square deviations:

\(7.76^2 = 60.2176\), \((-17.44)^2 = 304.1536\), \(0.16^2 = 0.0256\), \(0.76^2 = 0.5776\), \(8.76^2 = 76.7376\).

1. Sum squared deviations: \(60.2176 + 304.1536 + 0.0256 + 0.5776 + 76.7376 = 441.712\).
2. Divide by \(n - 1 = 4\): \(\frac{441.712}{4} = 110.428\).
3. Take square root: \(\sqrt{110.428} \approx 10.51\).

Answer:

Sample Mean: \(21.04\)
Median: \(21.80\)
Sample Standard Deviation: \(10.51\)