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

To calculate the standard deviation of a set of numbers, we follow a systematic process.

1. Analyze the question

We are given the dataset: 5, 4, 6, 7, 8. We need to find the standard deviation, which measures how spread out the numbers are from the mean.

2. Explain the concept

The formula for standard deviation ($\sigma$) is:

Where:

• $x$ = each individual score
• $\bar{x}$ = the mean (average) of the scores
• $n$ = the number of scores
• $\sum$ = the sum of the values

3. Show the solution

Step 1: Find the mean ($\bar{x}$)

Step 2: Subtract the mean from each score and square the result $(x - \bar{x})^2$

• $(5 - 6)^2 = (-1)^2 = 1$
• $(4 - 6)^2 = (-2)^2 = 4$
• $(6 - 6)^2 = (0)^2 = 0$
• $(7 - 6)^2 = (1)^2 = 1$
• $(8 - 6)^2 = (2)^2 = 4$

Step 3: Find the sum of these squares

Step 4: Divide by the number of scores ($n=5$)

Step 5: Take the square root to find the standard deviation

4. Identify the answer

Comparing our result to the given options, the correct choice is A.

5. Exam Tip

When calculating standard deviation, always remember that Variance = (Standard Deviation)². If you find the variance first, simply take the square root at the very end. Also, if your calculated mean is a whole number, the subtraction step becomes much faster and less prone to errors!