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.
To determine whether the given statements could apply to a data set consisting of 1,000 values that are all different, we need to understand what each statement represents and how to check it.
a. The 29th percentile is greater than the 30th percentile:
To check this statement, you would need to calculate the values of the 29th and 30th percentiles and compare them. The percentile represents the value below which a certain percentage of observations lie. If all the values are different in the data set, there will be a distinct value for each percentile.
b. The median is greater than the first quartile:
To check this statement, you would need to calculate the median and the first quartile and then compare them. The median is the value that separates the data into two equal halves, while the first quartile represents the point below which 25% of the values lie.
c. The third quartile is greater than the first quartile:
To check this statement, you would need to calculate the first quartile and the third quartile and then compare them. The third quartile represents the point below which 75% of the values lie.
d. The mean is equal to the median:
To check this statement, you would need to calculate the mean and the median and then compare them. The mean is the average of all the values in the data set, while the median is the middle value.
e. The range is zero:
To check this statement, you would need to calculate the range. The range is the difference between the maximum and minimum values in the data set. If all the values are different in the data set, the range will be non-zero.
By performing the necessary calculations and comparisons, you can determine if these statements apply to the given data set of 1,000 values that are all different.