3.Indicate whether each of the given statements could apply to a data set consisting of 1,000 values that are all different.

a. The 29th percentile is greater than the 30th percentile. (True or False)
b. The median is greater than the first quartile. (True or False)
c. The third quartile is greater than the first quartile. (True or False)
d. The mean is equal to the median. (True or False)
e. The range is zero. (True or False)

Oops! You forgot your answers. We'll be glad to check them for you.

a. To determine whether the 29th percentile is greater than the 30th percentile, you need to understand what the percentiles represent. Percentiles divide a data set into 100 equal parts. So, if all 1,000 values in the data set are different, each value will be in its own percentile. Therefore, the 29th percentile will be the 29th smallest value, and the 30th percentile will be the 30th smallest value.

In this case, since all the values are different, the 30th percentile will always be greater than the 29th percentile. Therefore, the statement is FALSE.

b. The first quartile (Q1) represents the 25th percentile, and the median represents the 50th percentile. In a data set with 1,000 different values, the median will be the value at the 500th percentile. Since the first quartile is at the 25th percentile, it will be a lower value than the median.

So, the statement that the median is greater than the first quartile is FALSE.

c. The first quartile (Q1) represents the 25th percentile, and the third quartile (Q3) represents the 75th percentile. In a data set with 1,000 different values, the first quartile will be a lower value than the third quartile.

So, the statement that the third quartile is greater than the first quartile is TRUE.

d. The mean is the average of all the values in the data set, while the median represents the middle value. In a data set with 1,000 different values, the mean may not be the same as the median, as it depends on the distribution of the values.

Thus, the statement that the mean is equal to the median is FALSE.

e. The range is the difference between the maximum and minimum values in the data set. Since all 1,000 values are different, the range will always be greater than zero.

Therefore, the statement that the range is zero is FALSE.