Chapter 6, Problem 36E

a)

To determine

To explain which one is better summary of the percentage of White residents in the neighborhoods.

Answer to Problem 36E

Median.

Explanation of Solution

Given:

  

The distribution is left skewed. Therefore, when the distribution is left skewed then the mean is more affected by the outlier points. Hence, median would better summary statistics as it is more resistant to skewed effects.

b)

To determine

To explain which one is better summary of the spread.

Answer to Problem 36E

IQR.

Explanation of Solution

Given:

  

The distribution is left skewed. Therefore, when the distribution is left skewed then the standard deviation is highly influenced by the outlier points. Hence, IQR would better summary statistics as it is more resistant to skewed effects.

c)

To determine

To find the percent of neighborhood within 1 standard deviation.

Answer to Problem 36E

The 68% of the values are within 1 standard deviation of the mean.

Explanation of Solution

Given:

  

According to rule of 68-95-99.7, the 68% of the values are within 1 standard deviation of the mean.

d)

To determine

To find the actual percent of neighborhood within 1 standard deviation.

Answer to Problem 36E

More than 80% of the values are within 1 standard deviation of the mean.

Explanation of Solution

Given:

  

Form Histogram, more than 80% of the neighborhoods have a white percentage greater than 61.33%. Therefore, about 80% of the data lies within 1 standard deviation from the mean.

e)

To determine

To explain discrepancy between part c and part d.

Answer to Problem 36E

The assumptions of Normal model do not fit so there is discrepancy between part c and d.

Explanation of Solution

Given:

  

As we know, the distribution is left skewed and we can not use Normal model for this distribution. That’s why there is discrepancy between part c and d.