Download Find the mean for the group of data items. Round to the nearest

Redwood High School. Department of Mathematics
Name:___________________________________
2015-2016 Advanced Algebra Test S2 #7 Statistics Prep wkst v2.0 .
Find the mean for the group of data items. Round to the nearest hundredth, if necessary.
1) 5.7, 8.3, 4.1, 7.8, 5.7, 1.1, 5.7, 3.2, 3.2, 3.7
1)
Find the mean for the data items in the given frequency distribution. Round to the nearest hundredth, if necessary.
2)
2)
Score
Frequency
x
f
1
3
2
4
3
5
4
9
5
8
6
6
7
12
8
7
9
11
10
11
Solve the problem.
3) Six people from different occupations were interviewed for a survey, and their annual
salaries were as follows: $12,000, $20,000, $25,000, $37,000, $67,500 and $125,000. What is
the median annual salary for the six people?
Find the mode for the group of data items.If there is no mode, so state.
4) 98, 98, 91, 32, 70, 98
3)
4)
For the given data set, find the a. mean b. median c. mode (or state that there is no mode) d. midrange.
5) Ages of teachers in the mathematics department of a certain high school:
5)
30, 55, 40, 56, 30, 55, 30, 46, 46, 43
Use the given frequency distribution to find the
(a) class width.
(b) class midpoints of the first class.
(c) class boundaries of the first class.
6)
6)
Height (in inches)
Class
Frequency, f
50 - 52
5
53 - 55
8
56 - 58
12
59 - 61
13
62 - 64
11
1
Use the given frequency distribution to construct a frequency histogram, and a frequency line histogram.
Height (in inches)
7)
7)
Class
Frequency, f
50 - 52
5
53 - 55
8
56 - 58
12
59 - 61
13
62 - 64
11
8) Kevin asked some of his friends how many hours they had worked during the previous
week at their after-school jobs. The results are shown below.
6 5 6 3 6 6 9 8 6 3 7 5
5 7 6 5 7 6 5 8 5 7 8 3
Construct a frequency distribution. Use 4 classes, a class width of 2 hours, and a lower limit
of 3 for
class 1.
Hours Frequency
Provide an appropriate response.
9) One purpose of displaying data graphically is to provide clues about trends. The given
values are weights (ounces) of steaks listed on a restaurant menu as "20 ounce porterhouse"
steaks. The weights are supposed to be 21 ounces because they supposedly lose an ounce
when cooked. Create a frequency distribution with 5 classes. Based on your distribution,
comment on the advertised "20 ounce" steaks.
17 20 21 18 20 20 20 18 19 19 20 19 21 20 18 20 20 19 18 19
Construct a frequency table for the given data.
10) The following is the number of hours students studied per week on average. Use five
intervals, starting with 0 - 4.
8)
9)
10)
2 8 12 15 24 22 16 11 7 1
5 10 18 24 15 14 5 10 15 20
Provide an appropriate response.
11) A student's score on the SAT-1 placement test for U.S. history is in the 90th percentile.
What can you conclude about the student's test score?
12) The numbers of home runs that Sammy Sosa hit in the first 15 years of his major league
baseball career are listed below. Make a stem-and-leaf plot for this data. What can you
conclude about the data?
4 15 10 8 33 25 36 40 36 66 63 50 64 49 40
2
11)
12)
13) The numbers of home runs that Barry Bonds hit in the first 18 years of his major league
baseball career are listed below. Make a stem-and-leaf plot for this data. What can you
conclude about the data?
16
33
25
42
24
40
19
37
33
34
25
49
34
73
46
46
13)
37
45
14) For the stem-and-leaf plot below, what is the maximum and what is the minimum entry?
14)
Key : 11 3 = 11.3
11
12
13
14
15
16
17
2
4
0
3
0
2
6
3
6
1
4
1
2
7
6
1
6
1
5
7
2
6
2
7
8
3
8
3
8
9
6
9
7
8
6
9
7
9
7 8 8
9
8 9
9
15) The numbers of home runs that Barry Bonds hit in the first 18 years of his major league
baseball career are listed below. Find the mean and median number of home runs. Round
the mean to the nearest whole number. Which measure of central tendency- the mean or
the median- best represents the data? Explain your reasoning.
16
33
25
42
24
40
19
37
33
34
25
49
34
73
46
46
15)
37
45
Determine the five-number summary of the given data.
16) The weekly salaries (in dollars) of sixteen government workers are listed below.
16)
690 604 813 647
728 585 476 623
519 675 685 456
547 787 512 826
17) The National Education Association collects data on the number of years of teaching
experience of high-school teachers. A sample taken this year of 19 high-school teachers
yielded the following data on number of years of teaching experience.
33 13 1 20 31
9 3 11 2 22
25 1 33 29 6
18 24 21 31
3
17)
Provide an appropriate response.
18) Without performing any calculations, use the stem-and-leaf plots to determine which statement is
accurate.
(i) 0
1
2
3
4
9
58
3377
25
1
(ii)
10
11
12
13
14
9
58
3377
25
1
(iii) 0
1 5
2 33337777
3 5
4
A) Data sets (i) and (iii) have the same range.
B) Data set (ii) has the greatest standard deviation.
C) Data set (i) has the smallest standard deviation.
D) Data sets (i) and (ii) have the same standard deviation.
19) Here are the batting averages of Sammy Sosa and Barry Bonds for 13 recent years. Which
player is more consistent? Explain your reasoning.
Sammy Sosa
Barry Bonds
0.300 0.268
0.312 0.294
0.203
0.292
0.273
0.308
0.260
0.311
0.251
0.291
19)
0.261
0.336
0.308 0.288 0.320 0.328 0.288 0.279
0.303 0.262 0.306 0.328 0.370 0.341
20) The test scores of 30 students are listed below. Find the five-number summary.
20)
31 41 45 48 52 55 56 58 63 65
67 67 69 70 70 74 75 78 79 79
80 81 83 85 85 87 90 92 95 99
21) The weights (in pounds) of 30 preschool children are listed below. Find the five-number
summary.
21)
25 25 26 26.5 27
27 27.5 28 28
28.5
29 29 30 30
30.5 31 31
32 32.5 32.5
33 33 34 34.5 35
35 37
37 38
38
22) Use the data to identify any outliers.
22)
34 42 57 65 66
69 71 72 74 77
79 82 87 90 99
23) Use the data to identify any outliers.
16
6
17
30
23)
27 1 32 15
18 9 20 14
19 16 10 21
14 39 18
4
18)
24) Use the data to identify any outliers.
24)
15 18 18 19 22 23 24
24 24 24 25 26 26 27
28 28 30 32 33 40 42
25) Use the box-and-whisker plot below to determine which statement is accurate.
25)
A) About 25% of the adults have cholesterol levels of at most 211.
B) One half of the cholesterol levels are between 180 and 211.
C) One half of the cholesterol levels are between 180 and 197.5.
D) About 75% of the adults have cholesterol levels less than 180.
Obtain the population standard deviation, , for the given data. Assume that the data represent population data. Round
your final answer to one more decimal place than that used for the observations.
26) The number of years of teaching experience is given below for 12 high-school teachers.
26)
26 29
17 8
22
5
10
13
12
22
19
31
Use this graph to answer the question.
Month
27) Which month in 1989 had the lowest sales?
27)
28) Which month in 1989 had the highest sales?
28)
29) What were the sales in month 11 of 1990?
29)
5
Use the data to make a frequency distribution table.
30) The following is the number of hours students studied per week on average.
30)
3 9 13 18 24 23 17 14 6 1
5 10 15 20 17 14 5 9 15 19
Frequency Distribution Table
Tally Frequency
0-4
5-9
10-14
15-19
20-24
Provide an appropriate response.
31) The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find the
interquartile range for the cholesterol level of the 30 adults.
31)
154 156 165 165 170 171 172 180 184 185
189 189 190 192 195 198 198 200 200 200
205 205 211 215 220 220 225 238 255 265
32) Use the data to identify any outliers.
32)
37 40 55 65 66
69 71 73 75 76
80 82 87 90 99
33) The test scores of 30 students are listed below. Draw a box-and-whisker plot that
represents the data.
33)
31 41 45 48 52 55 56 56 63 65
67 67 69 70 70 74 75 78 79 79
80 81 83 85 85 87 90 92 95 99
For the given data set, find the a. mean b. median c. mode (or state that there is no mode) d. midrange.
34) A company advertised that, on the average, 97% of their customers reported "very high
34)
satisfaction" with their services. The actual percentages reported in 15 samples were the
following:
97, 97, 92, 39, 75, 97, 92, 75, 97, 97, 39, 92, 92, 97, 39
a. Find the mean, median, mode and midrange. b. Which measure of central tendency was
given in the advertisement? c. Which measure of central tendency is the best indicator of
the "average" in this situation?
6
Answer Key
Testname: ADVALG S2 TEST 3 STATS WKS V3
1)
2)
3)
4)
5)
4.85
6.41
$31,000
98
a. 43.1
b. 44.5
c. 30
d. 43
6) (a) 3
(b) 51
(c) 49.5-52.5
7)
8)
Hours Frequency
3-4
3
5-6
13
7-8
7
9-10
1
9) Answers will vary. Possible answer: The frequency distribution shows that half of the cooked steaks are less than their
advertised weights.
10)
Interval Frequency
0-4
2
5-9
4
10 - 14
5
15 - 19
5
20 - 24
4
11) The student's score was higher than the scores of 90% of the students who took the test.
7
Answer Key
Testname: ADVALG S2 TEST 3 STATS WKS V3
12) Key: 0 4 = 4
0
1
2
3
4
5
6
4
0
5
3
0
0
3
8
5
6 6
0 9
4 6
Most of these years he hit 36 or more home runs.
13) Key: 1 6 = 16
1
2
3
4
5
6
7
6
4
3
0
9
5 5
3 4 4 7 7
2 5 6 6 9
3
Most of these years he hit between 33 and 49 home runs.
14) max: 17.7; min: 11.2
15) mean: 37; median: 35.5; The median best represents the data because the mean is affected by the
outlier (73) which causes a gap in the distribution.
16) 456, 533.0, 635.0, 709, 826
17) 1, 6, 20, 29, 33
18) D
19) Sosa: x = 0.279 and s = 0.033; Bonds: x = 0.312 and s = 0.027.
Bonds is more consistent since his standard deviation is less.
20) Min = 31, Q1 = 58, Q2 = 72, Q3 = 83, Max = 99
21) Min = 25, Q1 = 28, Q2 = 30.75, Q3 = 34, Max = 38
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
34, 42
1, 32, 39
40, 42
B
8.1
Month 3
Month 5
$70,000
Frequency: 2, 5, 4, 6, 3
31
37, 40
8
Answer Key
Testname: ADVALG S2 TEST 3 STATS WKS V3
33)
34) a. mean = 81.13, median = 92, mode = 97, midrange = 68
b. mode
c. mean
9