Standard Deviation Statistics Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
Calculate the population standard deviation of: 10, 12, 14.

Solution

  1. 1
    Step 1: Mean = 10+12+143=12\frac{10+12+14}{3} = 12. Squared deviations: (10โˆ’12)2=4,(12โˆ’12)2=0,(14โˆ’12)2=4(10-12)^2=4, (12-12)^2=0, (14-12)^2=4.
  2. 2
    Step 2: Variance = 4+0+43=83โ‰ˆ2.67\frac{4+0+4}{3} = \frac{8}{3} \approx 2.67. ฯƒ=2.67โ‰ˆ1.63\sigma = \sqrt{2.67} \approx 1.63.

Answer

ฯƒโ‰ˆ1.63\sigma \approx 1.63
Following the standard deviation formula step by step โ€” find the mean, compute squared deviations, average them, and take the square root.

About Standard Deviation

Standard deviation is a measure of how spread out data values are from the mean, representing the typical distance of data points from the average. A small standard deviation means data clusters tightly around the mean; a large one means data is widely spread.

Learn more about Standard Deviation โ†’

More Standard Deviation Examples

Example 1 medium

Calculate the population standard deviation of: 4, 8, 6, 2, 10.

Example 2 hard

Dataset A: {5, 5, 5, 5}. Dataset B: {2, 4, 6, 8}. Without full calculation, which has a larger stand

Example 4 medium

Calculate the population standard deviation of the data set: 3, 3, 7, 7.

โ† All Standard Deviation Examples Standard Deviation Concept