Calculate the standard deviation of the following scores 5, 4, 6, 7, and 8

Calculate the standard deviation of the following scores 5, 4, 6, 7, and 8

Answer Details

To calculate the standard deviation of a set of scores, we follow these steps:

1. Find the mean (average) of the scores:
   • Add all the scores together: 5 + 4 + 6 + 7 + 8 = 30.
   • Divide the total by the number of scores: 30 ÷ 5 = 6.
   Therefore, the mean is 6.
2. Calculate the squared differences from the mean:
   • For each score, subtract the mean and then square the result:
   • (5 - 6)² = 1
   • (4 - 6)² = 4
   • (6 - 6)² = 0
   • (7 - 6)² = 1
   • (8 - 6)² = 4
3. Find the average of these squared differences:
   • Add the squared differences together: 1 + 4 + 0 + 1 + 4 = 10.
   • Divide by the number of scores: 10 ÷ 5 = 2.
   This result is the variance, which is 2.
4. Take the square root of the variance to get the standard deviation:
   • √2.

The standard deviation of the scores 5, 4, 6, 7, and 8 is therefore √2, which is approximately 1.41, but following the options provided, the answer matches with √2.