Question

the mean is the \most sensitive\ average because it is affected by any change in the data.
a) determine the mean, median, mode, and midrange for 2, 3, 5, 6, 6, 9, 14.
b) change the 9 to 13 in part (a). determine the mean, median, mode, and midrange.
c) which averages were affected by changing the 9 to 13?
d) which averages will be affected by changing the 14 to 13 in part (a)?

a) select the correct choice below and fill in the answer boxes within your choice.
(round to the nearest tenth as needed. use a comma to separate answers as needed.)
a. the mean is , the median is , the mode(s) is/are , and the midrange is .
b. the mean is , the median is , there is no mode, and the midrange is .

Explanation:

Calculate the statistics for the original dataset

The dataset is: \(2, 3, 5, 6, 6, 9, 14\) (sorted, \(n = 7\)).

• Mean:

$$ \mu = \frac{2 + 3 + 5 + 6 + 6 + 9 + 14}{7} = \frac{45}{7} \approx 6.4 $$

• Median: The middle value (\(4^{\text{th}}\) value) is \(6\).
• Mode: The most frequent value is \(6\) (occurs twice).
• Midrange:

$$ \text{Midrange} = \frac{\text{min} + \text{max}}{2} = \frac{2 + 14}{2} = 8 $$

Match with the given multiple-choice options

• Option A states: "The mean is , the median is , the mode(s) is/are , and the midrange is ."
• Option B states: "The mean is , the median is , there is no mode, and the midrange is __."
• Since there is a mode (\(6\)), Option A is the correct choice.
• The values to fill in are: mean = \(6.4\), median = \(6\), mode = \(6\), midrange = \(8\).

Answer:

• A. The mean is 6.4, the median is 6, the mode(s) is/are 6, and the midrange is 8. (Correct answer)
• B. The mean is 6.4, the median is 6, there is no mode, and the midrange is 8.