Question

the distances (in yards) for nine holes of a golf course are listed below.
335 392 408 523 147 503 177 377 360
complete parts (a) through (d) below.
(a) find the mean and median of the data.
the mean of the data is 358.
the median of the data is 377.
(b) convert the distances to feet. then rework part (a).
the mean of the data in feet is 1074.
the median of the data in feet is 1131.
(c) compare the measures you found in part (b) with those found in part (a). what do you notice?
a. the difference between the mean in part (b) and the mean in part (a) is equal to the similar difference between the medians.
b. the mean and median in part (b) are three times the mean and median in part (a).
c. the mean and median in part (b) are not the mean and median in part (a) expressed in feet.
d. the ratio of the mean in part (b) to the mean in part (a) is not equal to the similar ratio of the medians.

Explanation:

Calculate the mean and median in yards

Using the Mean Calculation and Median Calculation knowledge points

$$ \text{Data in yards: } 147, 177, 335, 360, 377, 392, 408, 503, 523 $$

$$ \text{Mean} = \frac{147 + 177 + 335 + 360 + 377 + 392 + 408 + 503 + 523}{9} = \frac{3222}{9} = 358 $$

$$ \text{Median (5th value)} = 377 $$

Convert distances to feet and recalculate

Using the Linear Transformation of Data, Mean Calculation, and Median Calculation knowledge points

$$ 1 \text{ yard} = 3 \text{ feet} $$

$$ \text{Data in feet: } 441, 531, 1005, 1080, 1131, 1176, 1224, 1509, 1569 $$

$$ \text{Mean in feet} = 358 \times 3 = 1074 $$

$$ \text{Median in feet} = 377 \times 3 = 1131 $$

Compare the measures

Using the Linear Transformation of Data knowledge point

$$ \text{Mean in feet} = 3 \times \text{Mean in yards} \quad (1074 = 3 \times 358) $$

$$ \text{Median in feet} = 3 \times \text{Median in yards} \quad (1131 = 3 \times 377) $$

This shows that multiplying each data value by a constant scales both the mean and median by that same constant.

Analyze part (d) options

Since part (d) is cut off from the image, we address the visible parts (a) through (c). For part (c), the correct observation is that the mean and median in feet are three times the mean and median in yards.

Answer:

Question 1

The mean of the data is 358.
The median of the data is 377.

Question 2

The mean of the data in feet is 1074.
The median of the data in feet is 1131.

Question 3

• A. The difference between the mean in part (b) and the mean in part (a) is equal to the similar difference between the medians.
• B. The mean and median in part (b) are three times the mean and median in part (a). (Correct answer)
• C. The mean and median in part (b) are not the mean and median in part (a) expressed in feet.
• D. The ratio of the mean in part (b) to the mean in part (a) is not equal to the similar ratio of the medians.