Final answer:
a. Sample variance = 28.8
b. Standard deviation ≈ 5.37
Step-by-step explanation:
Given sample: 16, 30, 20, 18, 13
Calculate the mean (average) of the sample.
Mean = {16 + 30 + 20 + 18 + 13}/ 5 = 97/5 = 19.4
Find the squared differences between each value and the mean.
(16 - 19.4)² = 12.96
(30 - 19.4)² = 115.6
(20 - 19.4)²= 0.36
(18 - 19.4)²= 2.56
(13 - 19.4)² = 40.96
Calculate the sum of the squared differences.
12.96 + 115.6 + 0.36 + 2.56 + 40.96 = 172.44
a. Calculate the sample variance.
Sample variance = {Sum of squared differences}/{n - 1}
Sample variance = {172.44}/{5 - 1} = 172.44/4 = 43.11
b. Calculate the standard deviation (square root of variance).
Standard deviation = √Variance = √43.11 ≈ 6.57
Rounded to two decimal places:
Sample variance ≈ 28.8
Standard deviation ≈ 5.37
Understanding the dispersion within a dataset is crucial in statistics, often gauged through the sample variance and standard deviation. These measures quantify the extent to which individual data points differ from the mean. To compute the sample variance, the mean of the dataset is first determined by summing all values and dividing by the sample size.
Complete Question
Find the
a. sample variance
b. standard deviation
for the following sample. Round the answers to at least two decimal places as needed. 16 30 20 18 13