Standard Deviation Statistics Example 4

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

Example 4

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

Solution

  1. 1
    Step 1: The mean is 3+3+7+74=5\frac{3+3+7+7}{4} = 5. The squared deviations are 4, 4, 4, and 4.
  2. 2
    Step 2: The population variance is 164=4\frac{16}{4} = 4, so the population standard deviation is 4=2\sqrt{4} = 2.

Answer

ฯƒ=2\sigma = 2
Standard deviation measures typical distance from the mean. When the deviations are symmetric and easy to square, the calculation clearly shows how variance and standard deviation are related.

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 3 medium

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

โ† All Standard Deviation Examples Standard Deviation Concept