indicate whether the given statement 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.
b. the median is greater than the quartile
c. the third quartile is greater than the first quartile
d. the range is zero
Do you know your definitions of median (50th percentile), quartiles and range? Look them up in your text.
b. Which quartile?
To determine whether each statement could apply to a data set consisting of 1,000 values that are all different, we need to understand the concepts of percentiles, median, quartiles, and range.
a. The 29th percentile is greater than the 30th percentile:
To answer this question, we need to know how to calculate percentiles. Percentiles divide a data set into 100 equal parts. For example, the 29th percentile represents the value below which 29% of the data falls. The 30th percentile represents the value below which 30% of the data falls. Since the data set consists of 1,000 values that are all different, there will be a unique value for each percentile. Therefore, it is not possible for the 29th percentile to be greater than the 30th percentile since each percentile would correspond to a unique value. The answer is NO.
b. The median is greater than the quartile:
The median is the value that separates the data set into two equal halves. If the data set has an even number of values, the median is the average of the two middle values. Quartiles divide the data set into four equal parts. The first quartile represents the value below which 25% of the data falls, and the third quartile represents the value below which 75% of the data falls. Since all 1,000 values are different, the median, being in the middle, cannot be greater than any quartile. The answer is NO.
c. The third quartile is greater than the first quartile:
As mentioned earlier, quartiles divide the data set into four equal parts. The first quartile represents the value below which 25% of the data falls, and the third quartile represents the value below which 75% of the data falls. Since the data set consists of 1,000 values that are all different, the third quartile will always represent a higher value than the first quartile. Therefore, the answer is YES.
d. The range is zero:
The range of a data set is the difference between the maximum and minimum values. Since the data set consists of 1,000 values that are all different, there will be a difference between the maximum and minimum values. Therefore, it is not possible for the range to be zero. The answer is NO.
In summary:
a. NO, the 29th percentile cannot be greater than the 30th percentile.
b. NO, the median cannot be greater than any quartile.
c. YES, the third quartile is greater than the first quartile.
d. NO, the range cannot be zero.