(4) The distances (in yards) for nine holes of a golf course are listed below. 3
ID: 3204033 • Letter: #
Question
(4)
The distances (in yards) for nine holes of a golf course are listed below.
335 393 408 522 146 503 177 369 360
Find the mean and median of the data.
Convert the distances to feet. Then rework part
The mean of the data in feet is ?
The median of the data in feet is ?
Compare the measures you found in part (b) with those found in part (a). What do you notice?
The mean and median in part (b) are not the mean and median in part (a) expressed in feet.
B.The ratio of the mean in part (b) to the mean in part (a) is not equal to the similar ratio of the medians.
(d) Use your results from part (c) to explain how to quickly find the mean and median of the given data set when the distances are converted to inches.
A.
If you multiply the mean and median from part (a) by 3, you will get the mean and median of the data set in inches.
B.
If you convert all the distances to feet and then rework part (a), it will be the quickest way to obtain the mean and the median in inches.
C.
If you multiply the mean and median from part (a) by 12, you will get the mean and median of the data set in inches.
D.
If you multiply the mean and median from part (b) by 12, you will get the mean and median of the data set in inches.
(4)
Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found or a measure does not represent the center of the data, explain why.
The typing speeds (in words per minute) for several stenographers are listed below.
132 125 145 125 200 175 160 225 185 220
The mean typing speed is ……… words per minute
Does the mean represent the center of the data?
A.
The mean represents the center.
B.
The mean does not represent the center because it is not a data value.
C.
The mean does not represent the center because it is the smallest data value.
D.
The mean does not represent the center because it is the largest data value.
The median typing speed is……… words per minute?
Does the median represent the center of the data?
A.
The median represents the center.
B.
The median does not represent the center because it is the largest data value.
C.
The median does not represent the center because it is the smallest data value.
(6)
heights (in inches) of a sample of a species of tree two years after being planted are shown below.
18.8
19.8
18.4
16.6
18.9
16.4
19.1
19.1
14.7
14.7
17.7
17.7
Determine whether the data are qualitative or quantitative and identify the data set's level of measurement.
What is the data set's level of measurement?
Interval
Nominal
Ratio
Ordinal
(7)
An auction company sold 15 handheld computers last month. The final prices (in dollars) at which the items sold are as follows.
217
208
211,
249,
249
249,
229
229,
239,
253
248
229
229,
239,
249
Construct a stem-and-leaf plot. b. Summarize what this plot tells you about the data.
Stems
Leaves
20
21
22
23
24
25
Which of the following best summarizes what the stem-and-leaf plot tells you about the data?
A.
The plot does not show all the data. It only shows the prices that fall between
$208 and $ 253 inclusive.
B.
The plot does not show all the data. It only shows the prices that fall between
$ 200
and $260 inclusive.
C.
The plot gives an overview of all the data. It clearly shows that the prices fall between $200 and $260 inclusive.
D.
The plot gives an overview of all the data. It clearly shows that the prices fall between $208 and $ 253 inclusive.
18.8
19.8
18.4
16.6
18.9
16.4
19.1
19.1
14.7
14.7
17.7
17.7
Explanation / Answer
(4) (a) Mean = Sum of the values/Total number of values
= 3213/9 = 357
Arrange the numbers in ascending order.
146, 177, 335, 360, 369, 393, 408, 503,522
Middle item = 5th item = 369
So, median = 369
(b) Converting from yards to feet, we get:
438, 531, 1005, 1080, 1107, 1179, 1224, 1509, 1566
Mean = 9639/9 = 1071
Median = 5th item = 1107
(c) Mean & median in part (b) are the mean and median in part (a) expressed in feet.
B. Mean in (a)/Mean in (b) = 357/1071 = 0.3333
Median in (a)/Median in (b) = 369/1107 = 0.3333
The ratios are same.
To covert to inches:
Quick method:
Mean = 1071 X 12 = 12852
Median = 1107 X 12 = 13284
SINCE THE NUMBER OF QUESTIONS IS LARGE, ONLY THE FIRST FULL QUESTION IS ANSWERED AS PER DIRECTIONS FOR ANSWERING.
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