Download Math109 test1 Practice Qs soln

North Seattle Community College
2011
Winter
ELEMENTARY STATISTICS
2618 MATH 109 - Section 05, Chapter 1 and 2 - Practice Quiz 1
Questions and Solutions
1)
Identify population and sample in each of the following studies:
a) In a recent survey, 250 college students at Union College were asked if they
smoked cigarettes regularly.
b) The annual salary of each full-time professor at Florida State University
a) Sample
2)
b) Population
Determine whether the numerical values describe parameters or statistics:
a) A recent survey of a sample of 450 college students reported that the average
weekly income for students is $325.
b) The average weekly income for all students is $405.
a) Statistic, because it describes the characteristic of a sample
b) Parameter, because it describes the characteristic of the entire population
3) The grade point averages of five students are listed in the table. Which data are
qualitative data and which are quantitative data?
- Students names are qualitative. GPA is quantitative.
4) Determine level of measurement for each of the following?
a) Morning commute (in miles) of teachers at Midtown High School
b) Ocean temperature at seven beaches along the east coast of the U. S.
c) 1st, 2nd, and 3rd place finishers of the 2000 Boston Marathon
d) Account numbers of the clients of the S & H Bank
a) ratio
b) interval
c) ordinal
d) nominal
are quantitative data?
Student
GPA
Sally
3.22
Bob would you use3.98
5) Which method of data collection
for each of the following studies?
a) a study of the effect of Glucotrol
on a diabetics
Cindy
2.75 sugar control. Experiment
b) a study of the effect of electrical shock to the human body. Simulation
Mark
2.24
c) a study to determine the
average number of
children per couple in the U. S.
Survey
Kathy
3.84
a) Experiment
4) Determine
level of measurement for each of the following?
a)
Morning
commute (in miles) of teachers at Midtown High School
b) Simulation
b) Ocean temperature at seven beaches along the east coast of the U. S.
c) Survey
c) 1st, 2nd, and 3rd place finishers of the 2000 Boston Marathon
d) Account numbers of the clients of the S & H Bank
6) 5)You
are method
conducting
survey at
the you
college
you
attend
to determine
the number of
Which
of dataacollection
would
use for
each
of the following
studies?
a) who
a study
of the
effect of Glucotrol
on a diabetics
sugarconsists
control. of four campuses, one each
students
own
a personal
computer.
The college
a study of the effect of electrical shock to the human body.
on theb)
north,
south, east, and west sides of the city. Since you attend the south campus,
c) a study to determine the average number of children per couple in the U. S.
you decide to ask 200 of the 5,000 students from that campus. Which sampling
technique
didconducting
you use?a survey at the college you attend to determine the number of students who own a
6) You are
personal computer. The college consists of four campuses, one each on the north, south, east, and west sides
of
the city. Since sampling
you attend the south campus, you decide to ask 200 of the 5,000 students from that
Convenience
campus. Which sampling technique did you use?
7) 7)The
number of years of service of 60 randomly chosen Jacksonville firefighters is as
The number of years of service of 60 randomly chosen Jacksonville firefighters is as follows.
follows.
a) Find the missing values indicated in the table i), ii) and iii).
b) the
Calculate
the mean
andindicated
standard deviation
of the i),
years
service
a) Find
missing
values
in the table
ii) of
and
iii).for the 60 firefighters.
i)
ii)
iii)
60-(21+15+11) = 13
15/60 = 0.250
34 + 15 = 49
b) Calculate the mean and standard deviation of the years of service for the 60
firefighters.
i)
Sample mean = (3*21 + 8*13 + 13*15 + 18*11)/60 = (63+104+195+198)/60 =
9.33
ii)
Sample standard deviation = !!! =
!!"
!"#$.!!
!"
= 5.66
Classes
1-5
6-10
11-15
x
3
8
13
f
21
13
15
16-20
18
11
xf
63
104
195
198
60
560
Sum
(x--𝒙)2*f
841.45
23.00
202.03
826.86
1893.33
8) Which set of data is represented by the histogram below? (choose one)
a) 1, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6
b) 3, 5, 5, 8, 9, 11, 12, 13, 13, 14, 14, 15, 15, 17, 17, 17, 18, 18, 20
c) 1, 5, 6, 7, 9, 9, 10, 13, 13, 14, 14, 15, 15, 17, 18, 19, 20, 20
d) 4, 6, 7, 8, 9, 10, 10, 13, 13, 13, 14, 16, 17, 17, 18, 19, 20, 21
- b) 3, 5, 5, 8, 9, 11, 12, 13, 13, 14, 14, 15, 15, 17, 17, 17, 18, 18, 20
9) Suppose you are taking a class in which your final grade is figured as follows: 50%
from your test mean, 25% from your final exam score, 15% from your quiz mean, and
10% from your homework grade. If your grades are 80 (test mean), 88 (final exam), 75
(quiz mean), and 98 (homework), what is the weighted mean of your scores?
Weighted mean = 0.5*80+0.25*88+0.15*75+0.10*98=83.05
10) Construct an ordered stem-and-leaf diagram describing the following data: 106,
103, 107, 111, 113, 116, 113, 119, 119, 120, 125, 134, 136, 134.
Key 10|3 = 103
10 3,6,7
11 1,3,3,6,9,
12 0,5
9
13 4,4,6
11) Find the measures of central tendencies (mean, median, mode)
a) For the following lengths of operating times in months of 15 randomly selected car
batteries: 18, 21, 22, 22, 23, 23, 23, 25, 25, 26, 27, 30, 30, 31, 32.
i) Mean = 378/15=25.2
ii) Median =25
iii) Mode = 23
b) Suppose the last car battery sampled above lasted 60 months instead of 32 months.
Find the mean, median, mode of this new set of data.
Mean = 406/15=27.07
Median = 25
Mode = 23
c) How has the change in the data from a) to b) impact the mean, median and mode.
The mean increased from 25.2 by 2 units to 27.07 but this didn’t affect the median and
the mode thus indicating that the latter two measures are less sensitive to outliers.
12) Find the measures of variation (range, standard deviation, and variance) for the
following sample data: 5, 8, 9, 10, 15, 21, 27, 32
a) Range = 32-5 = 27
b) Standard deviation
Sum
x
5
8
9
10
15
21
27
32
127
(x-x)2
118.26
62.016
47.27
34.52
0.77
26.25
123.77
260.02
672.86
Mean = 127/8 =15.875
Standard Deviation , σ =
(!!!)!
!!!
=9.804
c) Variance = σ2 = 96.125
13) Suppose a data set has a mean of 8 and a standard deviation of 2. What proportion
of the data values are between
a) 2 and 14
b) 8 and 12
c) 6 and 8
mean µ=8, standard deviation, σ=2
Assuming the distribution is bell-shaped and symmetric.
(a) 95% of the values lie between (µ-3σ,µ+3σ) => (8-3*2,8+3*2)=>(2,14)
(b) We know that 95% of the values lies between 2σ of µ i.e. 95% lies between (82*2,8+2*2)=(4,12). One half of it is (8,12) which represents 95%/2 = 47.5%
(c) We know that 64% of the values lies between 1σ of µ i.e. 64% lies between (81*2,8+1*2)=(6,10). One half of it is (6,8) which represents 64%/2 = 34%
14) A set of bell-shaped distributed data has mean 500 and standard deviation 40.
Between what two values does approximately 95% of the data lie?
2 standard deviations on each side of the mean represents 95% of the data i.e. 420 to
580
15) The mean price of houses in a certain neighborhood is $100,000, and the standard
deviation is $10,000.
Find the price range for which at least 75% of the houses will sell.
Using Chebychev’s theorem is the probability that 75% of the data lies within 2 standard
deviations of the mean,
i.e. (𝜇 − 2 ∗ 𝜎, 𝜇 + 2 ∗ 𝑠𝜎) = (100000-2*10000, 100000+2*10000)
=(80000, 120000)
16) Identify the following histograms as symmetric, uniform, skewed-left, skewedright: (a)
(b)
(c)
skew-left,
skew-right,
symmetric
17) For questions (a) through (g), please refer to the sample data below. The following
are GPA’s of randomly selected students. The values are sorted from low to high. { 1.54,
1.59, 1.67, 1.86, 1.94, 2.06, 2.08, 2.43, 2.53, 2.63, 2.91, 2.93, 3.05, 3.12, 3.32, 3.54, 3.80,
3.81, 4.00 }.
a) Compute the sample mean.
Sample mean=50.81/19=2.67
b) Compute the standard deviation and variance.
x
1.54
1.59
1.67
1.86
1.94
2.06
2.08
2.43
2.53
2.63
2.91
2.93
3.05
3.12
3.32
3.54
3.8
3.81
4
(x-mean)
-1.134210526
-1.084210526
-1.004210526
-0.814210526
-0.734210526
-0.614210526
-0.594210526
-0.244210526
-0.144210526
-0.044210526
0.235789474
0.255789474
0.375789474
0.445789474
0.645789474
0.865789474
1.125789474
1.135789474
1.325789474
(x-mean)^2
1.286433518
1.175512465
1.008438781
0.662938781
0.539065097
0.377254571
0.35308615
0.059638781
0.020796676
0.001954571
0.055596676
0.065428255
0.141217729
0.198728255
0.417044044
0.749591413
1.267401939
1.290017729
1.757717729
11.42786316
Variance =0.634881287
Standard deviation =0.796794382
c) Compute the median.
Median is the value corresponding to the (n+1)/2 = 10th value = 2.63
d) Compute the mode.
No mode
e) Compute the range.
Range = Max – Min = 4-1.54=2.46
f) Compute the lower (Q1) and upper quartiles (Q3) and the inter-quartile range
Q1=Average between 5th and 6th values = (1.94+2.06 )/2 = 2
Q3=Average between 15th and 16th values = (2.63+2.91)2 = 2.77
IQR = 2.77-2 = .77
g) Construct a frequency table and histogram, with the first lower class limit equal to
1.54. Use 5 classes.
Class
1.54-2.03
2.04-2.53
2.54-3.03
3.04-3.53
3.54-4.03
midpoint
1.785
2.285
2.785
3.285
3.785
frequency
5
4
4
3
4
relative
cumulative
frequency frequency
0.25
5
0.2
9
0.2
13
0.15
16
0.2
20
18) A student receives the following grades, with an A worth 4 points, a B worth 3 points,
a c worth 2 points and a D worth 1 point. What is the student’s mean grade point score?
A in 1 four-credit class
B in 2 three-credit classes
C in 1 three-credit class
D in 1 two-credit class
Grade
A
B
B
C
D
Points, x
4
3
3
2
1
Credits, w
4
3
3
3
3
Σw = 15
x.w
16
9
9
6
3
Σ x.w= 43
Mean score = 43/15 = 2.6875
19) A salesperson at a company sold $6,903,435 of hardware equipment last year, a
figure that represented the eighth decile of sales performance at the company. What can
you conclude about the salesperson’ performance?
The performance is good because 80% of the sales peoples sold less than this
salesperson.
20) Assuming equal ranges and sample sizes, will a set of bell-shaped distributed data or
a set of uniformly distributed data have the greater standard deviation. Explain your
reasoning.
The bell-shaped distribution has relatively more data near the mean than the uniform
distribution. So to cover 68% of the data, one would need to travel farther from the mean
in the uniform distribution than the bell shaped distribution, so the uniform distribution
has a larger standard deviation.