Question

for the data shown, answer the questions. round to 2 decimal places.
x
8.9
28.5
19.3
12.2
1.9
26
23.5
18.1

compute the sample mean:
compute the median:
compute the sample standard deviation:
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Explanation:

Sample Mean Calculation

Step1: Sum all data points

Sum = \( 8.9 + 28.5 + 19.3 + 12.2 + 1.9 + 26 + 23.5 + 18.1 \)
\( = 138.4 \)

Step2: Divide by number of data points (n=8)

Mean = \( \frac{138.4}{8} \)
\( = 17.3 \)

Median Calculation

Step1: Order the data

Ordered data: \( 1.9, 8.9, 12.2, 18.1, 19.3, 23.5, 26, 28.5 \)

Step2: Find middle (n=8, even)

Median = \( \frac{18.1 + 19.3}{2} \)
\( = \frac{37.4}{2} = 18.7 \)

Sample Standard Deviation Calculation

Step1: Find deviations from mean

Deviations: \( 8.9 - 17.3 = -8.4 \), \( 28.5 - 17.3 = 11.2 \), \( 19.3 - 17.3 = 2 \), \( 12.2 - 17.3 = -5.1 \), \( 1.9 - 17.3 = -15.4 \), \( 26 - 17.3 = 8.7 \), \( 23.5 - 17.3 = 6.2 \), \( 18.1 - 17.3 = 0.8 \)

Step2: Square the deviations

Squared deviations: \( (-8.4)^2 = 70.56 \), \( 11.2^2 = 125.44 \), \( 2^2 = 4 \), \( (-5.1)^2 = 26.01 \), \( (-15.4)^2 = 237.16 \), \( 8.7^2 = 75.69 \), \( 6.2^2 = 38.44 \), \( 0.8^2 = 0.64 \)

Step3: Sum squared deviations

Sum = \( 70.56 + 125.44 + 4 + 26.01 + 237.16 + 75.69 + 38.44 + 0.64 \)
\( = 577.94 \)

Step4: Divide by (n - 1) = 7

Variance = \( \frac{577.94}{7} \approx 82.5629 \)

Step5: Take square root

Standard Deviation = \( \sqrt{82.5629} \approx 9.09 \)

Answer:

s:
Sample Mean: \( 17.30 \)
Median: \( 18.70 \)
Sample Standard Deviation: \( 9.09 \)