How To Convert A Mean Score To A Percentage

Mean scores determine the average performances of students or athletes, amongst other applications. You can convert mean scores to percentages that indicate the average percentage of the score relative to the total score. You can also convert mean scores to percentages to show the performance of a score relative to a specific score. Comparing a mean score to the highest score with a percentage is useful for statistical analysis.

1. Find Mean Score

Find the mean score if not already determined. Add all the scores (​x​₁, ​x​₂, ​x​₃ and so on, the ​x​_i values) and divide by the total number of scores or "​n​" to find the mean score. The formula is:

\(\text{mean} = \frac{\sum_i x_i}{n}\)

2. Find the Comparison

Determine the score you want to compare the mean score to. You may compare the mean score with the highest possible score, the highest score or a specific score. For example, say you want to compare a mean score of 65 to the highest score of 98.

3. Apply Division

Divide the mean score by the score you chose in step 2. Work out

\(\frac{65}{98} = 0.6632\)

4. Convert Decimal to Percentage

Multiply the decimal you obtain in step 3 by 100 to convert to a percentage. Work out

\(0.66 × 100 = 66.32\)

Round the percentage to the nearest whole number (66) if you wish. Your mean score as a percentage is 66 percent.