Standard Deviation Statistics Example 1

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

Example 1

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

Solution

  1. 1
    Step 1: Mean = 4+8+6+2+105=6\frac{4+8+6+2+10}{5} = 6.
  2. 2
    Step 2: Squared deviations: (4โˆ’6)2=4,(8โˆ’6)2=4,(6โˆ’6)2=0,(2โˆ’6)2=16,(10โˆ’6)2=16(4-6)^2=4, (8-6)^2=4, (6-6)^2=0, (2-6)^2=16, (10-6)^2=16.
  3. 3
    Step 3: Variance = 4+4+0+16+165=405=8\frac{4+4+0+16+16}{5} = \frac{40}{5} = 8. Standard deviation = 8โ‰ˆ2.83\sqrt{8} \approx 2.83.

Answer

ฯƒโ‰ˆ2.83\sigma \approx 2.83
Standard deviation measures the typical distance of data points from the mean. It is the square root of the average of squared deviations, giving a measure of spread in the same units as the data.

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 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.

Example 4 medium

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

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