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.
To indicate whether the given statements apply to a data set consisting of 1,000 values that are all different, we can use some basic concepts and calculations in statistics. Let's go through each statement one by one:
a. The 29th percentile is greater than the 30th percentile.
To answer this, we need to determine whether the data set has evenly spaced values. Since the data set consists of 1,000 different values, it is highly unlikely that the values will be evenly spaced. Therefore, we cannot conclude that the 29th percentile would be greater than the 30th percentile.
b. The median is greater than the first quartile.
The median represents the middle value of a sorted data set, while the first quartile is the value that divides the lowest 25% of the data from the highest 75%. In a data set with 1,000 different values, the median will be the 500th value, and the first quartile will be the 250th value. Therefore, it is indeed possible that the median could be greater than the first quartile.
c. The third quartile is greater than the first quartile.
Similar to the previous statement, both the first quartile and third quartile are based on the position of values in a data set. In a data set with 1,000 different values, the first quartile (Q1) will be the 250th value, and the third quartile (Q3) will be the 750th value. As such, it is highly likely that the third quartile will be greater than the first quartile.
d. The mean is equal to the median.
The mean and median are two different measures of central tendency. The mean is calculated by summing up all the values in the data set and then dividing by the total number of values. The median, as mentioned earlier, is the middle value of a sorted data set. For a data set with 1,000 different values, it is highly unlikely that the mean will be exactly equal to the median.
e. The range is zero.
The range is the difference between the highest and lowest values in a data set. Since the data set consists of 1,000 different values, it is highly unlikely that the highest and lowest values will be the same. Thus, the range will not be zero.
In summary, based on the given data set with 1,000 different values:
a. Cannot be determined.
b. Possible.
c. Likely.
d. Unlikely.
e. Not possible.