Question

1. consider the set of numbers given.

25, 33, 8, 18, 16
a sixth value of 20 is added to the data set. fill in the blank with \increase\, \decrease\, or \stay the same\ to indicate what will happen as a result of including this new value. give a reason for your answer.
a. the mean will decrease
b. the median will

c. the range will stay

d. the standard deviation will

1. forty students were asked to report the time of their commute to school, in minutes. the data are shown in the dot - plot

a. the mean commute time to school is 14.2 minutes. how does the median commute time compare to this value? explain your reasoning.
b. which measure of center, mean or median, would best describe the typical commute time to school? explain.
c. the standard deviation of commute times for these 40 students is 14.4 minutes. interpret this value.

Explanation:

Step1: Arrange original data in ascending order

$8, 16, 18, 25, 33$

Step2: Calculate original median

Since there are 5 numbers, the median is the 3rd - numbered value, so the original median is $18$.

Step3: Add new value and arrange new - data in ascending order

The new data set is $8, 16, 18, 20, 25, 33$.

Step4: Calculate new median

Since there are 6 numbers, the median is the average of the 3rd and 4th - numbered values. $\frac{18 + 20}{2}=19$.
So the median will increase.

Step5: Analyze range

The original range is $33−8 = 25$. The new range is $33−8 = 25$. So the range will stay the same.

Step6: Analyze standard deviation

The standard deviation measures the spread of the data. The new value $20$ is closer to the center of the original data set. The overall spread of the data will decrease. So the standard deviation will decrease.

Answer:

b. increase
c. stay the same
d. decrease