A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative ability. For the verbal ability test, the mean for people in general is 50 and the standard deviation is 20. For the quantitative ability test, the mean for people in general is 0 and the standard deviation is 5. Which is this person’s stronger ability: verbal or quantitative? Expalin your answer to a person who has never had a course in statistics.
Calculate Z score for both tests and compare.
Z = (X - μ)/SD, where X = score, μ = mean and SD = standard deviation.
The Z score give the person's relative position in a group of scores.
I hope this helps. Thanks for asking.
To determine which ability is stronger for this person, we can compare their scores to the mean scores of the general population and consider the standard deviations.
First, let's understand what the mean and standard deviation represent:
- Mean: The mean is the average score of the general population. It gives us a baseline to compare individual scores against.
- Standard Deviation: The standard deviation measures the spread or dispersion of scores around the mean. It helps us understand how much individual scores vary from the average.
Now, let's analyze the person's scores:
1. Verbal Ability:
- The person scored 81 on the verbal ability test.
- The mean for the general population is 50, indicating an average verbal ability.
- The standard deviation is 20, suggesting that there is a moderate amount of variability in verbal ability scores.
2. Quantitative Ability:
- The person scored 6.4 on the quantitative ability test.
- The mean for the general population is 0, indicating an average quantitative ability.
- The standard deviation is 5, indicating that there is relatively less variability in quantitative ability scores compared to verbal ability scores.
Now, let's compare the individual scores to the mean scores and consider the standard deviations:
- Verbal Ability: The person scored 31 points above the mean (81 - 50), which is higher than one standard deviation (20) above the mean. This suggests that the person's verbal ability is relatively strong compared to the general population.
- Quantitative Ability: The person scored 6.4 points above the mean (6.4 - 0), which is less than one standard deviation (5) above the mean. This suggests that the person's quantitative ability is closer to the average in comparison.
Based on this analysis, we can conclude that the person's stronger ability is verbal, as they performed significantly better in verbal ability compared to the average population, while their quantitative ability is closer to the average.