The standard deviation of the numbers of oranges in the 7 crates is SD = 0 because there is no variability between the number of oranges in each crate.
Determining the the standard deviation
Let's consider the information given:
Statement 1: The median of the numbers of oranges was equal to the greatest of the numbers of oranges.
Statement 2: The range of the numbers of oranges was 0.
From statement 2, we know that the range (the difference between the greatest and smallest values) of the numbers of oranges was 0. This implies that all the crates contained the same number of oranges, as the difference between the greatest and smallest values (range) is 0. Therefore, each crate must have had the same number of oranges.
Now, statement 1 says that the median of the numbers of oranges was equal to the greatest of the numbers of oranges. Since each crate had the same number of oranges, the median (middle value) would also be the same as the greatest value.
In a set of seven identical values (in this case, the number of oranges in each crate), the median will be the same as the greatest value. Therefore, both statements provide consistent information indicating that all crates had the same number of oranges.
Since all crates had the same number of oranges, and the number of oranges in each crate is identical, the standard deviation of the numbers of oranges in the 7 crates is SD = 0 because there is no variability between the number of oranges in each crate.
A store received 7 crates of oranges. What was the standard deviation of the numbers of oranges in the 7 crates?
(1) For the 7 crates of oranges, the median of the numbers of oranges was equal to the greatest of the numbers of oranges.
(2) For the 7 crates of oranges, the range of the numbers of oranges was 0.