3. 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 first quartile.
c. The third quartile is greater than the first quartile.
d. The mean is equal to the median.
e. The range is zero.
In any distribution, the median (50th percentile) is always higher than the first quartile (25th percentile) and the third quartile (75th percentile) is greater than the first quartile.
The 29th percentile is always less than the 30th percentile.
The mean = median only in a normal distribution.
Range = 0 only if all the scores are identical.
Two of the answers apply.
By the way, note the correct spelling above.
Standard deviation for the following sets
and compare the differences.
first 7 #'s 57 61 57 57 58 57 61
second 7#'s 61 52 69 64 46 54 47
First 7"s = 1
The second 7's = 5.75
I got the same answer for standard deviation, except the 5.75 should be rounded to the nearest tenth.
To determine whether the given statements apply to a data set consisting of 1,000 values that are all different, we need to understand the definitions and calculations of the statistical terms involved.
a. The 29th percentile is greater than the 30th percentile:
To calculate percentiles, we arrange the data in ascending order and find the value below which a certain percentage of data falls. Since all the 1,000 values are different, each percentile would correspond to a unique value. Therefore, it is not possible for the 29th percentile to be greater than the 30th percentile. This statement does not apply to the given data set.
b. The median is greater than the first quartile:
The median is the middle value of the data set when arranged in ascending order. The first quartile represents the 25th percentile, which is the value below which 25% of the data falls. In a data set with 1,000 different values, the median would correspond to the 500th value, while the first quartile would correspond to the 250th value. As the values are unique and arranged in ascending order, it is not possible for the median to be greater than the first quartile. This statement does not apply to the given data set.
c. The third quartile is greater than the first quartile:
Similarly, in a data set with 1,000 different values, the first quartile would correspond to the 250th value, and the third quartile would correspond to the 750th value. As the values are unique and arranged in ascending order, it is possible for the third quartile to be greater than the first quartile. This statement could apply to the given data set.
d. The mean is equal to the median:
The mean is the average of all the values in the data set, while the median is the middle value. In a perfectly symmetrical data set, the mean and median would be equal. However, since the data set consists of 1,000 different values, it is highly unlikely for the mean to be exactly equal to the median. This statement does not apply to the given data set.
e. The range is zero:
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, it is highly unlikely for the range to be exactly zero. This statement does not apply to the given data set.
In summary, statement c (The third quartile is greater than the first quartile) is the only statement that could apply to a data set consisting of 1,000 values that are all different.