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? Explain your answer to a person who has never had a course in statistics.

Start by finding the z scores.

z = (value - mean)/SD

verbal: z = (81-50)/20
z = 1.55

quantitative: z = (6.4-0)/5
z = 1.28

Compare the z scores. 1.55 > 1.28. Therefore, the person's score exceeded the mean by more in the verbal test.

To determine which ability, verbal or quantitative, is stronger for this person, we need to compare their scores to the mean and standard deviation of the respective tests.

For the verbal ability test:
1. Calculate the z-score for the person's score using the formula:
z = (X - μ) / σ
where X is the person's score, μ is the mean, and σ is the standard deviation.
For this person, X = 81, μ = 50, and σ = 20.
z = (81 - 50) / 20
= 31 / 20
= 1.55

2. Similarly, calculate the z-score for the quantitative ability test:
X = 6.4, μ = 0, and σ = 5.
z = (6.4 - 0) / 5
= 6.4 / 5
= 1.28

Now, let's explain the concept of z-scores to someone who has never had a course in statistics:

Z-scores are a way to measure how far a particular data point is from the mean of a dataset in terms of standard deviations. It helps us understand whether a data point is above or below average and by how much.

In our case, a z-score of 1.55 for the verbal ability test means that the person's score is 1.55 standard deviations above the mean. On the other hand, a z-score of 1.28 for the quantitative ability test means that the person's score is 1.28 standard deviations above the mean.

Since a z-score of 1.55 is higher than 1.28, it indicates that the person's verbal ability score is relatively stronger compared to their quantitative ability score. In simpler terms, if we consider the distribution of scores, the person's verbal score is further to the right (higher) than their quantitative score.

Therefore, based on this analysis, we can conclude that the person's stronger ability is verbal.

To determine which ability is stronger for this person, we can compare their scores to the mean and standard deviation for each test. In this case, we have the following information:

Verbal ability test:
- Person's score = 81
- Mean for people in general = 50
- Standard deviation = 20

Quantitative ability test:
- Person's score = 6.4
- Mean for people in general = 0
- Standard deviation = 5

To measure the strength of an ability, we usually consider how far a person's score is from the average (mean) and how spread out the scores are (standard deviation).

For the verbal ability test, the person's score of 81 is higher than the mean score of 50. This indicates that the person performed well above the average on this test.

For the quantitative ability test, the person's score of 6.4 is also higher than the mean score of 0. However, since the standard deviation for this test is only 5, it means that the scores are not very spread out. Therefore, even though the person scored higher than the mean, it may not necessarily indicate a strong quantitative ability compared to others.

In conclusion, based on the given scores and statistical measures, the person's stronger ability is verbal, as they performed well above the average and the scores are more spread out on this test.