Question

4. The data shows the time in seconds for 8 runners competing in the 100-meter dash at Saturday's track meet. [14, 13, 16, 15, 12, 14, 13, 15] What value describes the mean of the data?

5. which statement is true about the measures of center?
A:) The median and mean are equivalent, so the shape of the distribution is symmetric.
B:) The mean is greater than the median, so the shape of the distribution is skewed.
C:) The median is greater than the mean, so the shape of the distribution is non-symmetric.
D:) You cannot determine any information about the shape of the distribution using the measures of center.

6. which of the following could NOT be used to describe a measure of spread?
F:) 4
G:) 13 to 15
H:) 12 to 16
J:) 14

Bonus:) The only info I have so far is the order of the numbers which is 12, 13, 13, 14, 14, 15, 15, 16.

Answer 1

Step-by-step explanation: To find the mean of the data, we add up all the values and divide by the number of values:

(14 + 13 + 16 + 15 + 12 + 14 + 13 + 15) / 8 = 14

So the mean of the data is 14.

B) The statement "The mean is greater than the median, so the shape of the distribution is skewed" is generally true. However, there are some cases where the mean and median can be equal and the distribution can still be skewed, so the statement is not always true.

F) 4 cannot be used to describe a measure of spread since it is a single number and does not provide any information about the range or variability of the data.

Bonus: Given the ordered data set [12, 13, 13, 14, 14, 15, 15, 16], we can determine several measures of center and spread. The median is 14 since it is the middle value when the data is ordered. The mean is also 14 since the sum of the values divided by 8 is 112/8 = 14. The range is 16 - 12 = 4, and the interquartile range (IQR) is the difference between the first and third quartiles. The first quartile (Q1) is the median of the lower half of the data, which is (12 + 13 + 13 + 14) / 4 = 13, and the third quartile (Q3) is the median of the upper half of the data, which is (14 + 15 + 15 + 16) / 4 = 15. So the IQR is 15 - 13 = 2.