Answer :
To determine which country likely has the greatest difference between the incomes of the rich and the poor, we need to consider the role of standard deviation in a data set.
1. Mean income: The mean income of both Japan and England is the same, at $51,000. The mean is a measure of the central tendency or average income in each country.
2. Standard deviation: The standard deviation is a measure of the spread or dispersion of incomes around the mean. A higher standard deviation indicates that the incomes are more spread out from the mean, while a lower standard deviation suggests that the incomes are closer to the mean.
Given that the standard deviation of incomes in Japan is greater than that of England, we can infer the following:
- Greater Spread in Japan: Since the standard deviation in Japan is higher, it implies that the incomes in Japan are more widely spread out from the mean of $51,000. This means there is a larger variation in incomes, and the differences between the poorest and richest individuals are more pronounced.
- Smaller Spread in England: Conversely, with a lower standard deviation in England, the incomes are clustered more closely around the mean. This suggests less variation in incomes and a smaller difference between the poorest and richest individuals.
Therefore, the country with the greatest difference between the incomes of the rich and the poor is Japan.
So, the correct answer is:
- Japan
1. Mean income: The mean income of both Japan and England is the same, at $51,000. The mean is a measure of the central tendency or average income in each country.
2. Standard deviation: The standard deviation is a measure of the spread or dispersion of incomes around the mean. A higher standard deviation indicates that the incomes are more spread out from the mean, while a lower standard deviation suggests that the incomes are closer to the mean.
Given that the standard deviation of incomes in Japan is greater than that of England, we can infer the following:
- Greater Spread in Japan: Since the standard deviation in Japan is higher, it implies that the incomes in Japan are more widely spread out from the mean of $51,000. This means there is a larger variation in incomes, and the differences between the poorest and richest individuals are more pronounced.
- Smaller Spread in England: Conversely, with a lower standard deviation in England, the incomes are clustered more closely around the mean. This suggests less variation in incomes and a smaller difference between the poorest and richest individuals.
Therefore, the country with the greatest difference between the incomes of the rich and the poor is Japan.
So, the correct answer is:
- Japan
