1. [0.6/0.6 Points]
PREVIOUS ANSWERS
AUFEXC XXXXXXXXXXMI. 1/100 Submissions Used
MY NOTES
ASK YOUR TEACHER
DETAILS
Find the mean, the median, and the mode(s), if any, for the given data. Round noninteger means to the nearest tenth. (If there is more than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.)
−8.1, −2.6, 4.5, 4.5, 6.6, 8.9, 9.5
mean XXXXXXXXXXmedian XXXXXXXXXXmode(s)
Additional Materials
Tech Guide: Excel Tech Guide: TI-83/84 Tech Guide: TI-Nspire
On a reading test, Shaylen's score of 455 was higher than the scores of 4246 of the 7244 students who took the test. Find the percentile, rounded to the nearest percent, for Shaylen's score.59
th percentile
8/14/2021
Week 7: Practice HW 7: XXXXXXXXXXMATH 115, section D04, Summer 1 2021 | WebAssign
https:
www.webassign.net/we
Student/Assignment-Responses/last?dep= XXXXXXXXXX
2/22
The following tables list the ages of female and male actors when they sta
ed in their award-winning Best Actor performances. (A graphing calculator is recommended.)
Ages of Best Female Actor Award Recipients
62
55
45
78
22
71
57
21
79
70
21 34
40
53
77
21
56
69
28
26
36
71
55
46
48
31
59
76
37
52
79
32
43
73
Ages of Best Male Actor Award Recipients
62
75
53
59
66
40
72
64
44
51
71 43
74
63
61
49
39
49
72
67
43
52
73
56
34
52
66
41
73
38
70
39
51
32
(a) Find the mean and the sample standard deviation of the ages of the female recipients. Round each result to the nearest tenth.
mean
50.7
50.7
y
sample standard deviation
19.3
19.3
y
(b) Find the mean and the sample standard deviation of the ages of the male recipients. Round each result to the nearest tenth.
mean
56.4
55.7
y
sample standard deviation
13.3
13.3
y
(c) Which of the two data sets has the larger mean?female actors male actors
Which of the two data sets has the larger standard deviation? female actors male actors
Consider the following.
5, 25, 6, 12, 13, 26
Compute the population standard deviation of the numbers. (Round your answer to two decimal place.)8.30
(a) Double each of your original numbers and compute the standard deviation of this new population. (Round your answer to two decimal place.)16.60
(b) Use the results of part (a) and inductive reasoning to state what happens to the standard deviation of a population when each data item is multiplied by a positive constant k.The standard deviation is divided by k. The standard deviation is multiplied by k. The standard deviation is unchanged.
The standard deviation is multiplied by -k.
The standard deviation is k.
A survey of 10 fast-food restaurants noted the number of calories in a mid-sized hamburger. The results are given in the table below.
Calories in a mid-sized hamburge
514 506 503 499 497 505 458 479 463 514
Find the mean and sample standard deviation of these data. Round to the nearest hundredth.
mean20.17
493.80
sample standard deviation
Additional Materials
Tech Guide: Excel Tech Guide: TI-83/84 Tech Guide: TI-Nspire
Another measure of central tendency for a set of data is called the midrange. The midrange is defined as the value that is halfway between the minimum data value and the maximum data value. That is,
Midrange = minimum value + maximum value .
2
The midrange is often stated as the average of a set of data in situations in which there are a large amount of data and the data are constantly changing. Many weather reports state the average daily temperature of a city as the midrange of the temperatures achieved during that day. For instance, if the minimum daily temperature of a city was 60° and the maximum daily temperature
was 90°, then the midrange of the temperatures is 60° + 90° = 75°.
2
During a two-minute period, the temperature in a town increased from a low of −6°F to a high of 49°F. Find the mid-range of the temperatures during this two-minute period.21.5
°F
The table below shows the numbers of bushels of barley cultivated per acre for 12 one-acre plots of land for two different strains of barley, PHT-34 and CBX-21.
PHT-34
CBX-21
42
55
49
47
47
43
38
45
46
46
44
50
50
47
46
59
46
52
45
50
44
48
43
52
Using the same scale, draw a box-and-whisker plot for each of the two data sets, placing the PHT-34 plot below the CBX-21 plot.
Write a valid conclusion based on the data.
The median number of bushels cultivated per acre for CBX-21 is approximately equal to the median number of bushels cultivated per acre for PHT-34.
The maximum number of bushels cultivated per acre for PHT-34 is approximately equal to the median number of bushels cultivated per acre for CBX-21.
The maximum number of bushels cultivated per acre for CBX-21 is approximately equal to the median number of bushels cultivated per acre for PHT-34.
The minumum number of bushels cultivated per acre for PHT-34 is approximately equal to the median number of bushels cultivated per acre for CBX-21.
Additional Materials
Tech Guide: TI-83/84 Tech Guide: TI-Nspire
8/14/2021
Week 7: Practice HW 7: XXXXXXXXXXMATH 115, section D04, Summer 1 2021 | WebAssign
https:
www.webassign.net/we
Student/Assignment-Responses/last?dep= XXXXXXXXXX
10/22
Stem-and-Leaf Diagrams
The relative position of each data value in a small set of data can be graphically displayed by using a stem-and-leaf diagram. For instance, consider the following history test scores.
65, 72, 96, 86, 43, 61, 75, 86, 49, 68, 98, 74, 84, 78, 85, 75, 86, 73
In the stem-and-leaf diagram below, we have organized the history test scores by placing all of the scores that are in the 40s in the top row, the scores that are in the 50s in the second row, the scores that are in the 60s in the third row, and so on. The tens digits of the scores have been placed to the left of the vertical line. In this diagram, they are refe
ed to as stems. The ones digits of the test scores have been placed in the proper row to the right of the vertical line. In this diagram, they are the leaves. It is now easy to make observations about the distribution of the scores. Only two of the scores are in the 90s. Six of the scores are in the 70s, and none of the scores are in the 50s. The lowest score is 43, and the highest is 98.
A Stem-and-Leaf Diagram of a Set of History Test Scores
Stems
Leaves
4
3 9
5
6
1 5 8
7
XXXXXXXXXX
8
XXXXXXXXXX
9
6 8
Legend: 8|6 represents 86
The choice of how many leading digits to use as the stem will depend on the particular data set. For instance, consider the following data set, in which a travel agent has recorded the amount spent by customers for a cruise.
Amount Spent for a Cruise, Summer of 2012
$3600
$4700
$7200
$2100
$5700
$4400
$9400
$6200
$5900
$2100
$4100
$5200
$7300
$6200
$3800
$4900
$5400
$5400
$3100
$3100
$4500
$4500
$2900
$3700
$3700
$4800
$4800
$2400
One method of choosing the stems is to let each thousands digit be a stem and each hundreds digit be a leaf. If the stems and leaves are assigned in this manner, then the notation 2|1, with a stem of 2 and a leaf of 1, represents a cost of $2100, and 5|4 represents a cost of $5400. A stem-and-leaf diagram can now be constructed by writing all of the stems in a column from smallest to largest to the left of a vertical line and writing the co
esponding leaves to the right of the line. See the diagram below.
Amount Spent for a Cruise
Stems
Leaves
2
1 1 4 9
3
XXXXXXXXXX
4
XXXXXXXXXX
5
XXXXXXXXXX
6
2 2
7
2 3
8
9
4
Legend: 7|3 represents $7300
Sometimes two sets of data can be compared by using a back-to-back stem-and-leaf diagram, in which common stems are listed in the middle column of the diagram. Leaves from one data set are displayed to the right of the stems, and leaves from the other data set are displayed to the left. For instance, the back-to-back stem-and-leaf diagram below shows the test scores for two classes that took the same test. It is easy to see that the 8 A.M. class did better on the test because it had more scores in the 80s and 90s and fewer scores in the 40s, 50s, and 60s. The number of scores in the 70s was the same for both classes.
Biology Test Scores
8 A.M. class
10 A.M. class
2
4
5 8
7
5
6 7 9 9
5 8
6
2 3 4 8
XXXXXXXXXX
7
XXXXXXXXXX
XXXXXXXXXX
8
XXXXXXXXXX
XXXXXXXXXX
9
4 5
Legend: 3|7 represents 73
Legend: 8|2 represents 82
Watch the video below then answer the question.
Stem-and-Leaf Diagrams
Construct a back-to-back stem-and-leaf diagram for the winning and losing scores given in the table below. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)
Super Bowl Results, 1967–2011
35–10
33–14
16–7
23–7
16–13
24–3
14–7
24–7
16–6
21–17
32–14
27–10
35–31
31–19
27–10
26–21
27–17
38–9
38–16
46–10
39–20
42–10
20–16
55–10
20–19
37–24
52–17
30–13
49–26
27–17
35–21
31–24
34–19
23–16
34–7
20–17
48–21
32–29
24–21
21–10
29–17
17–14
27–23
31–17
31–25
Winning Scores vs. Losing Scores
Winning
Losing
2 5
2 6 8 9
XXXXXXXXXX XXXXXXXXXX
5
4
3
none
none
1
XXXXXXXXXX XXXXXXXXXX
2
XXXXXXXXXX9
XXXXXXXXXX
1
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
none
0
XXXXXXXXXX
What information is revealed by your diagram?Most of the winning scores are in the 20s and 30s, whereas most of the losing