1) the following represents the algebra test scores of 20 students: 29, 31, 67, 67, 69, 70, 71, 72,...
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1) The following represents the Algebra test scores of 20 students: 29, 31, 67, 67, 69, 70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90, 91, 91, 93.
a) Create a stem-leaf.
Stem
leaf
2 9
3 1
6 7 7 9
7 0 1 2 5 7 8
8 0 3 5 7
9 0 0 1 1 3
1) The following represents the Algebra test scores of 20 students: 29, 31, 67, 67, 69, 70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90, 91, 91, 93.
b) Create a histogram.
1) The following represents the Algebra test scores of 20 students: 29, 31, 67, 67, 69, 70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90, 91, 91, 93.
c) What is the mean, mode, and median?
Mean: 74.8Mode: 67, 90, 91Median: 77.5
1) The following represents the Algebra test scores of 20 students: 29, 31, 67, 67, 69, 70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90, 91, 91, 93.
d) Create a box-plot.
2969.5 77.2 88.5
93
1) The following represents the Algebra test scores of 20 students: 29, 31, 67, 67, 69, 70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90, 91, 91, 93.
e) What is the interquartile range?
f) What is the standard deviation?
Q3 – Q1 = 88.5 – 69.5 = 19
Standard Deviaion = 17.17
1) The following represents the Algebra test scores of 20 students: 29, 31, 67, 67, 69, 70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90, 91, 91, 93.
g) Suppose that a 21st score of 5 is added. Which will likely change the most: mean, mode, or median?
Will the standard deviation increase or decrease?
mean
increase
1) The following represents the Algebra test scores of 20 students: 29, 31, 67, 67, 69, 70, 71, 72, 75, 77, 78, 80, 83, 85, 87, 90, 90, 91, 91, 93.
h) Describe the shape, center, and spread of this data.
negatively skewed
2) Describe the shape of the following distributions. Use words like skewed to
the left (less numbers on the left), skewed to the right (less numbers to the right), uniform, unimodel (one mode tower),
bimodal (two mode towers), gap, outlier, symmetric, and bell shaped.A
B
A: ___________________________
B: ___________________________
skewed right
skewed left
2) Describe the shape of the following distributions. Use words like skewed to
the left (less numbers on the left), skewed to the right (less numbers to the right), uniform, unimodel (one mode tower),
bimodal (two mode towers), gap, outlier, symmetric, and bell shaped.
C
gap
2) Describe the shape of the following distributions. Use words like skewed to
the left (less numbers on the left), skewed to the right (less numbers to the right), uniform, unimodel (one mode tower),
bimodal (two mode towers), gap, outlier, symmetric, and bell shaped.
D
bell
3) Use the following box-plot to answer the questions:
a) What is the interquartile range?
b) What is the maximum?
c) What is the minimum?
80 90 100
110
120
130
140
150
160
170
95 145
145 – 95 = 50
about 162
80
3) Use the following box-plot to answer the questions:
d) Draw a histogram that best models this box-plot.
80 90 100
110
120
130
140
150
160
170
4) A set of data has a mean of 56.7 and a standard deviation of 2.5. What would the new mean and new standard deviation be if each set of data is increased by 5?
New mean: 61.7Standard Deviation: 2.5
5) The following data shows the ages of teachers: 23, 25, 25, 27, 29, 30, 31, 32, 33, 34, 36, 37, 40, 41, 42, 43, 55
a) What measure of spread is more appropriate for this data (mean, mode, median, or standard deviation)?
b) Are there any outliers? Explain.
c) Describe the shape of this data.
mean
Q3 – Q1 = 40.5 – 28 = 12.5 = IQR1.5(12.5) = 18.75
skewed right (positive)
40.5 + 18.75 = 59.25Since none of the data is less than 9.25 nor
greater than 59.25, there are NO outliers.
28 – 18.75 = 9.25
6) A teacher interviewed 200 students and found the following results:
Male Female
Sophomore
.2 .1
Junior .1 .25
Senior .25 .1
a) How many senior males did the teacher interview?
b) If the student was a sophomore, what gender was the student more likely to be?
c) How many more female juniors were there than male juniors?
= 40
= 20
= 50
= 20
= 50= 20
50
male
30
7) The following are test scores of a Biology test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73, 74, 76, 77, 78, 82, 88, 93, 94, 95.
a) Create a stem-leaf.
Stem
leaf
5 5 9
6 0 1 5 5 5
7 0 2 3 4 6 7 8
8 2 8
9 3 4 5
7) The following are test scores of a Biology test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73, 74, 76, 77, 78, 82, 88, 93, 94, 95.b) Create a histogram.
7) The following are test scores of a Biology test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73, 74, 76, 77, 78, 82, 88, 93, 94, 95.
c) What is the mean, mode, and median?
Mean = 73.79
Mode = 65Median = 73
7) The following are test scores of a Biology test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73, 74, 76, 77, 78, 82, 88, 93, 94, 95.
d) Create a box-plot.
5565 73 82
95
7) The following are test scores of a Biology test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73, 74, 76, 77, 78, 82, 88, 93, 94, 95.
e) What is the interquartile range?
f) What is the standard deviation?
IQR = 82 – 65 = 17
12.3 or 11.9
7) The following are test scores of a Biology test: 55, 59, 60, 61, 65, 65, 65, 70, 72, 73, 74, 76, 77, 78, 82, 88, 93, 94, 95.
g) Suppose that a 21st score of 5 is added. Which will likely change the most: mean, mode, or median?
Will the standard deviation increase or decrease?
mean
increase
Use the following box-plot to answer the questions:
8)
10 12 14 16 18 20 22 24 26
a) What is the interquartile range?
b) What is the maximum and minimum?
12 16
IQR = 16 – 12 = 4
Maximum = 26Minimum = 10
A set of data has a mean of 44.7 and a standard deviation of 1.3. What would the new mean and new standard deviation be if each of the data is decreased by 3?
9)
New mean = 41.7
Standard Deviation = 1.3
The following data shows household income: 23500, 26000, 28000, 29000, 32500, 36500, 38500, 42200, 55000, 58500, 62000, 67000, 112200.
10)
a) What measure of spread is more appropriate for this data (mean, mode, median, or standard deviation)?
b) Are there any outliers? Explain.
c) Describe the shape of this data.d) Suppose that a millionaire is added to the data set, which measure of spread will increase the most?
medianQ3 – Q1 = 60250 – 28500 = 31750
= IQR1.5(31750) = 47625
60250 + 31750 = 107875112200 is an outlier.
skewed right
mean
400 people were surveyed. Each person was asked whether he or she prefers Drama or Comedy movies. The results are shown in the relative frequency table below:
11)
Age Drama Comedy
Total
21-30 .25 .30 .55
31-40 .15 .06 .2141 .20 .04 .24
Total .6 .4 1a) How many more people prefer drama than comedy?b) How many more 21-30 year olds prefer comedy than drama?
c) How many total people prefer drama?
= 100= 60
= 80
= 240
= 120= 24= 16
= 160
= 220= 84
= 96
240 – 160 = 80
120 – 100 = 20 240
Match the following histogram (E-H) to the correct box-plot (A-D):
12) A
B
C
D
E
F
G H
G
H
F
E
The following shows the population of various towns (in thousands)?
13)
City East North
South
West Center
Wayout
Salem
Population
(thousands)
30 40 56 48 51 53 64
Suppose that Winstonville with a population of 26,000 is added to the data set. Which of the following is true?A) The mean increases.
B) The range remains the same.C) The standard deviation increases.D) The interquartile range increases.
A chair lift can hold a maximum of 40000 pounds and 200 people. A safety inspector is determining if the chair lift is safe or not. Which measure of central tendency of people’s weight would be the most useful to determine if the chair lift is safe?
14)
A) Mean
B) MedianC) ModeD) Standard Deviation
The number of points scored by a football team in the first eight games of the season are: 10, 14, 17, 20, 35, 35, 38, 42. What would happen to the data distribution if the team scored 27, 27, and 28 in the next three games.
15)
A) The standard deviation would increase.B) The data distribution would become more peaked and more widely spread.
C) The data distribution would become less peaked and less widely spread.
D)The data distribution would become more peaked
and less widely spread.
Which of the following is most likely to have the highest standard deviation? To have the lowest interquartile range?
16)
A) The average age of 100 people surveyed at the mall.
B) The average age of 100 people living in a retirement center.
C) The weight of 100 new-born babies.
D) The amount of TV’s that 100 households have.
highest standard deviation
lowest interquartile range
Which of the following statements is true?
17)
A) A data set with high standard deviation means that there is low variability.B) A data set with low standard deviation means that the data set is spread out.C) As the amount of data increases, the standard deviation usually increases.
D) A data set with many outliers will have a high standard deviation.
Which of the following data sets has the highest interquartile range? Lowest standard deviation?
18)
A) Integers from 1-20
B) Even integers from 2-40
C) The prime numbers from 1-100
D) List of ages of 20 different teenagershighest interquartile range
lowest standard deviation
The math club has 50 members. Each member was asked if he preferred Algebra or Geometry. The results are shown in the relative frequency table:
19)
Geometry Algebra TotalUnderclassme
n.36 .28 .64
Upperclassmen
.04 .32 .36
Total .4 .6 1.00Which is true?A) Eight more underclassmen prefer Geometry than Algebra.B) Thirty-six students are upperclassmen.
C) Fourteen more upperclassmen prefer Algebra than Geometry.
D) 32 % of the students preferred Algebra.
= 18
= 30= 20
= 14
= 16= 2= 50
= 32
= 18