Emily,Zeke,Harry,& Brook each conducted surveys on the number of books people have
in their homes. Then they answered the question below.
"MUST ALL MEASURES OF CENTRAL TENDENCY
APPEAR AS A NUMBER IN A SET OF DATA COLLECTED?
A. Emily says this is always true because all the measures of central tendency also have to be in the numbers in the set of data.
B.Zeke says this is never true because all the measures of central tendency are never numbers in the set of data.
C.Harry says this is sometimes true because the mean and median may or may not be in the set of data, but the mode is always in the set of data.
D. Brook says this is sometimes true because the mean and mode may or may not
be in the set of data, but the median is always in the set of data.
WHY?
To determine which statement is correct, we need to understand the different measures of central tendency and whether they must always appear as a number in a set of data.
The measures of central tendency include the mean, median, and mode, which are calculated to represent the typical or central value of a data set.
A. Emily says this is always true because all the measures of central tendency also have to be in the numbers in the set of data.
This statement is incorrect. The measures of central tendency do not necessarily have to be one of the numbers in the set of data. The mean, for example, is calculated by summing all the values and dividing by the total number of values, which may not be an actual value in the data set.
B. Zeke says this is never true because all the measures of central tendency are never numbers in the set of data.
This statement is also incorrect. While it is true that the measures of central tendency may not always be a number in the set of data, this does not mean that it never occurs.
C. Harry says this is sometimes true because the mean and median may or may not be in the set of data, but the mode is always in the set of data.
This statement is partially correct. The mode is indeed a value that appears in the set of data. It represents the value that occurs most frequently. However, the mean and median may or may not be numbers in the set of data. The mean is the average of the values and may not be a specific value in the data set. The median is the middle value when the data set is sorted and may or may not be one of the numbers in the set of data.
D. Brook says this is sometimes true because the mean and mode may or may not be in the set of data, but the median is always in the set of data.
This statement is incorrect. While the median is always a value in the set of data, both the mean and mode can be calculated as values that are not necessarily in the data set.
Therefore, the correct answer is C. Harry's statement that the mean and median may or may not be in the set of data, but the mode is always in the set of data.