Question

Leonard runs a study with a sample of 20 participants. The average score is 8.5 points, but he made a recording mistake for one participant, changing the score from X=6 to X=9. What is the new mean of Leonard's sample?

Answer 1

After correcting Leonard's mistaken recording from a score of 9 to 6, the new mean score for his sample of 20 participants becomes 8.35 points.

Step-by-step explanation:

When correcting Leonard's recording mistake, we need to adjust the total sum of scores and then recalculate the mean. The incorrect total sum was calculated with the score of 9 instead of the actual 6. To find the correct total sum, we subtract the incorrect score and add the correct one:

• Old total sum = average score × number of participants = 8.5 × 20 = 170
• Incorrect recorded score subtracted: 170 - 9 = 161
• Correct score added: 161 + 6 = 167

Now, we can calculate the new mean by dividing the corrected total sum by the number of participants:

• New mean = corrected total sum ÷ number of participants = 167 ÷ 20 = 8.35

Therefore, after correcting the recording mistake, the new mean score for Leonard's sample is 8.35 points.