3. Which statement is true about the following set of data?
18, 17, 21, 24, 21
a.The mean is greater than the median.
b.The median is less than the mode.
c.The mean and median are the same number.
d.The median and the mode are the same number.
For the defnition of the median of a set, see
http://www.mathwords.com/m/median_of_a_set_of_numbers.htm
The mean is the average value. Add them up and divide by 5. In this case, it is 20.2
The mode is the number that appears most often. Can you guess what that is? In this case it is the same as the mean.
To find which statement is true about the given set of data (18, 17, 21, 24, 21), we need to calculate the mean, median, and mode.
1. Mean: To find the mean, we need to sum up all the numbers and divide the sum by the total number of values. Let's calculate the mean for this data set:
Mean = (18 + 17 + 21 + 24 + 21) / 5
Mean = 101 / 5
Mean = 20.2
2. Median: To find the median, we need to arrange the numbers in ascending order and find the middle value. If there are two middle values, we find their average. Let's arrange the data set in ascending order:
17, 18, 21, 21, 24
Since there are five numbers, the middle value would be the third value, which is 21. Therefore, the median is 21.
3. Mode: The mode is the number that appears most frequently in the data set. In this case, the number 21 appears twice, which is more than any other number. Therefore, the mode is 21.
Now, let's evaluate each statement:
a. The mean is greater than the median.
This statement is false because the mean (20.2) is less than the median (21).
b. The median is less than the mode.
This statement is false because the median (21) is equal to the mode (21).
c. The mean and median are the same number.
This statement is false because the mean (20.2) is not equal to the median (21).
d. The median and the mode are the same number.
This statement is true because the median (21) is equal to the mode (21).
Therefore, the correct statement is d. The median and the mode are the same number.