Question

What is the population_variance of the data 116, 140, 152, 112, 144, 104?
60
O 345.25
6992
0 296.45
6160
O 325.33
0271.25​

Answer 1

Answer:

325.33

Step-by-step explanation:

population variance of given data is 325.33

Answer 2

Concept:

The population variance (σ²) describes how data points in a given population are distributed. It's the squared average of the distances between each population data point and the mean.

Given:

The given observations are 116, 140, 152, 112, 144, 104.

Find:

Find the population variance of the given data.

Solution:

Population variance is usually represented as σ² and can be calculated using the following formula:

σ² = $\frac{1}{N}$ ∑($x_{i}$ - μₓ)²

Here N is the population size and the $x_{i}$ are data points. μₓ is the population mean.

Step 1: Find the mean, μₓ.

μₓ $=\frac{116+140+152+112+144+104}{6}$

μₓ $=\frac{768}{6}$

μₓ $=128$

Step 2: Subtract each data point from the mean and then square the result.

$(128-116)^{2}=(12)^{2} \\(128-140)^{2}=(-12)^{2}\\(128-152)^{2= (-24)^{2}}\\(128-112)^{2}=(16)^{2}\\(128-144)^{2}=(-16)^{2}\\(128-104)^{2}=(24)^{2}$

Step 3: Sum up all of the squared differences from Step 2.

$144+144+576+256+256+576=1952$

Step 4: Divide Step 3 by the number of items to get the population variance.

Population variance $=\frac{1952}{6}$

Population variance $=325.33$

Hence the population variance of the given items is 325.33.