Datasets
Consider a set of three values: 5, 5, 8. What is the Mean, Population Variance, and Median for the dataset?
Expand Hint
The mean is the average of all the data points. The median is the value separating the higher half from the lower half of the data set.
Hint 2
Population variance:
$$$\sigma^2=\frac{1}{N}\sum_{i=1}^{N}(X_i-\mu )^2$$$
where
$$\mu$$
is the arithmetic mean of a discrete population size
$$N$$
, and
$$X_i$$
is the value of the individual observation.
The median is 5, which is the value that separates the higher half from the lower half of the dataset.
To find the mean of the values:
$$$\mu=\frac{sum\:of\:terms}{number\:of\:terms}=\frac{5+5+8}{3}=\frac{18}{3}=6$$$
Population variance:
$$$\sigma^2=\frac{1}{N}\sum_{i=1}^{N}(X_i-\mu )^2$$$
where
$$\mu$$
is the arithmetic mean of a discrete population size
$$N$$
, and
$$X_i$$
is the value of the individual observation.
$$$\sigma^2=\frac{2(5-6)^2+(8-6)^2}{3}=\frac{2(-1)^2+(2)^2}{3}=\frac{2+4}{3}=2$$$
Mean = 6; Median = 5; Variance = 2
Time Analysis
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