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)
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1. 91 10/16
2. 0
3.6,610
4.71.5
5.7/6
6.1/2
To answer each statement, we need to understand the concepts of percentiles, the median, quartiles, mean, and range.
a. The 29th percentile is greater than the 30th percentile. (True or False)
To determine the percentiles, we need to arrange the data in ascending order. Since the data set consists of 1,000 different values, percentiles correspond to specific positions in the sorted list. Assuming the data set ranges from the 1st to the 1,000th value, the 29th percentile would be the value at the position 290, and the 30th percentile would be the value at position 300 in the sorted list. Since the data set consists of distinct values, the 30th percentile will be greater than the 29th percentile, so the statement is false.
b. The median is greater than the first quartile. (True or False)
The median is the middle value when the data set is arranged in ascending order. Since the data set consists of 1,000 distinct values, the median is the value at position 500. The first quartile is the value at the 25th percentile or position 250. Since the median is greater than the first quartile position, the statement is true.
c. The third quartile is greater than the first quartile. (True or False)
The third quartile is the value at the 75th percentile, or position 750, while the first quartile is the value at the 25th percentile, or position 250. Since the third quartile is at a higher position in the sorted list than the first quartile, the statement is true.
d. The mean is equal to the median. (True or False)
To check if the mean is equal to the median, we need to find the mean and median of the 1,000 values. The mean is obtained by summing all the values and dividing by the total count (1,000 in this case). The median is the middle value after sorting the data. Since the data set consists of distinct values, the mean and median will not be equal unless all the values are the same. Therefore, the statement is generally false for a data set of 1,000 different values.
e. The range is zero. (True or False)
The range is the difference between the maximum and minimum values in the data set. Since the data set consists of 1,000 different values, the range will not be zero unless all the values are the same. Therefore, the statement is false.
In summary:
a. False
b. True
c. True
d. False
e. False