Emily, Zeke, Harry, and Brook each conducted surveys on the number of books people have in their homes. Then, each student determined the accuracy of the following statement.
All measures of central tendency must appear as a number in the set of data collected.
Which student’s statement is CORRECT?
A.
Zeke says this is never true because all the measures of central tendency are never numbers in the set of data.
B.
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.
C.
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.
D.
Emily says this is always true because all the measures of central tendency also have to be numbers in the set of data.
A is not always true. The mean in a data could be a value that's in the data for example (like if the mean was 20 and if 20 appeared in the data).
B must be true because the mode in a data set is the most frequent data value. If there is no mode, then there's no mode.
C is not correct. You can still find the median in a set of data without the median itself.
D is not true because it's basically the opposite of why A is wrong.
d
is incorrect. See the explanation above for why it is not a correct statement.
B
B is the correct answer. See the explanation above for why it is a correct statement.
To determine which student’s statement is correct, let's first understand what measures of central tendency are and whether they must appear as numbers in the set of data.
Measures of central tendency are statistical values that represent the center or typical value of a data set. The three commonly used measures of central tendency are the mean, median, and mode.
Now, let's evaluate each student’s statement:
A. Zeke says this is never true because all the measures of central tendency are never numbers in the set of data.
This statement is incorrect. It is possible for some measures of central tendency to be numbers in the set of data.
B. 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 always a number in the set of data, as it represents the value that appears most frequently. However, the mean and median may or may not be in the set of data.
C. 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 partially correct. The median is always a number in the set of data, as it represents the middle value when the data set is arranged in order. However, the mean and mode may or may not be in the set of data.
D. Emily says this is always true because all the measures of central tendency also have to be numbers in the set of data.
This statement is incorrect. While it is true that some measures of central tendency may appear as numbers in the set of data, not all measures necessarily do.
After evaluating each student’s statement, we can conclude that the correct statement is C. Brook's statement. The median is always a number in the set of data, but the mean and mode may or may not be in the set of data.