Question
In: Statistics and Probability
Problem 1. A set of 25 measurements consists of the values 3 6 7 15 12...
Problem 1. A set of 25 measurements consists of the values
3 6 7 15 12
6 8 4 5 6
5 12 1 3 3
7 5 10 8 3
9 2 6 1 5
(a) Construct a relative frequency histogram to describe the data.
(10 pts) (b) Find: the
median m (5 pts), the sample mean ¯x (5 pts), the sample standard
deviation s (5 pts), the
upper and lower quartiles (10 pts), the 37-th percentile (5 pts).
(c) Apply Tchebisheff’s
Theorem in order to estimate the proportion of measurements that
lie in the interval
[¯x − (1.5)s, ¯x + (1.5)s] (10 pts).
Solutions
Expert Solution
| x | frequency(f) | relative frequency(rf) | cumulative frequency(c.f.) | fx |  |
|---|---|---|---|---|---|
| 1 | 2 | 2/25 | 2 | 2 | 51.6128 |
| 2 | 1 | 1/25 | 3 | 2 | 16.6464 |
| 3 | 4 | 4/25 | 7 | 12 | 37.9456 |
| 4 | 1 | 1/25 | 8 | 4 | 4.3264 |
| 5 | 4 | 4/25 | 12 | 20 | 4.6656 |
| 6 | 4 | 4/25 | 16 | 24 | 2.56 |
| 7 | 2 | 2/25 | 18 | 14 | 1.6928 |
| 8 | 2 | 2/25 | 20 | 16 | 7.3728 |
| 9 | 1 | 1/25 | 21 | 9 | 8.5264 |
| 10 | 1 | 1/25 | 22 | 10 | 15.3664 |
| 12 | 2 | 2/25 | 24 | 24 | 70.0928 |
| 15 | 1 | 1/25 | 25 | 15 | 79.5664 |
a) Histogram
b) N=25
N/2=12.5
c.f. greater than 12.5 is 16 corresponding to x=6. Thus, median is 6.
N/4=6.25 ; cf greater than 6.25 is 7 which corresponds to x=3. Thus, lower quartile(Q1) = 3
3N/4=18.75; cf greater than 18.75 is 20 which corresponds to x=8. Thus, upper quartile(Q3) = 8
37N/100=9.25; cf greater than 9.25 is 12 which corresponds to x=5. Thus, 37-th percentile(P37) = 5
c) Tchebisheff's theorem is 
Thus, k=1.5
Substituting these values in tchebisheff's inequality, we get
orchestra answered 1 year agoRelated Solutions
For the data set 1 2 3 4 7 7 7 8 11 12 12 15...
For the data set
1
2
3
4
7
7
7
8
11
12
12
15
15
16
17
17
17
18
20
20
22
24
24
25
26
26
26
26
27
30
32
32
33
34
34
36
38
39
43
44
45
46
47
47
48
51
52
52
53
54
54
54
55
56
58
58
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61
63
65
65
67
69
70
73
75
75
76
77
77
79
80
81
82
82
(a)...
1, 1, 1, 1, 1, 3, 3, 3, 3, 6, 6, 6, 7, 7, 7, 12,...
1, 1, 1, 1, 1, 3, 3, 3, 3, 6, 6, 6, 7, 7, 7, 12, 12, 13, 17
1) Use three arguments to explain the character of the shape of
the distribution.
2) Determine the presence of outliers in either bound of the
distribution by the Fences Criterion.
3) Determine the presence of outliers in either bound using the
Z-scores criterion.
4) Summarize data in general.
3 6 4 8 1 10 2 9 11 12 15 22 3 6 7 5...
3
6
4
8
1
10
2
9
11
12
15
22
3
6
7
5
8
1
12
14
Each column represents a different treatment given to sick rats.
Each cell is a different rat. Use statistical analysis and use post
hoc testing using contrasts to find the best
treatment.
Treatment 1: vitamins
Treatment 2: prescription pills
Treatment 3: brain surgery
Treatment 4: shock therapy
Treatment 5: dietary changes
33. A population consists of the following scores: 12, 1, 10, 3, 7, 3 A....
33. A
population consists of the following scores: 12,
1, 10, 3, 7, 3
A. Compute m and s
for the population.
B. Find the
z-score for each raw score in the population.
C. Transform each
score into a new standardized value so that the standardized
distribution has a mean of m = 100 and a standard deviation of s =
20.
Do parts A, B, and
C, and then from part C, choose which new...
33. A population consists of the following scores: 12, 1, 10, 3, 7, 3 A....
33. A
population consists of the following scores: 12,
1, 10, 3, 7, 3
A. Compute m and s
for the population.
B. Find the
z-score for each raw score in the population.
C. Transform each
score into a new standardized value so that the standardized
distribution has a mean of m = 100 and a standard deviation of s =
20.
Do parts A, B, and
C, and then from part C, choose which new...
Here is a set of sample data. 3 87 7 57 15 90 25 55 68...
Here is a set of sample data.
3
87
7
57
15
90
25
55
68
70
89
20
26
93
9
5
86
23
37
52
96
4
91
Base on the data above, identify the 5 number summary
_ , _ ,_ , _ , _
For the following data set [ 1, 4, 3, 6, 2, 7, 18, 3, 7, 2,...
For the following data set [ 1, 4, 3, 6, 2, 7, 18, 3, 7, 2, 4,
3, 5, 3, 7] please compute the following
1. measures of central tendency (3 points)
2. standard deviation ( 5 points)
3. is 18 an outlier? (5 points)
4. describe the shape of the distribution (2 points)
n = 8 measurements: 5, 3, 6, 7, 6, 5, 4, 7 Calculate the sample variance,...
n = 8
measurements: 5, 3, 6, 7, 6, 5, 4, 7
Calculate the sample variance, s2, using the
definition formula. (Round your answer to four decimal places.)
s2 =
Calculate the sample variance, s2 using the
computing formula. (Round your answer to four decimal places.)
s2 =
Find the sample standard deviation, s. (Round your
answer to three decimal places.)
s =
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18%...
Periods
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
15%
16%
18%
20%
1
0.990
0.980
0.971
0.962
0.952
0.943
0.935
0.926
0.917
0.909
0.893
0.877
0.870
0.862
0.847
0.833
2
0.980
0.961
0.943
0.925
0.907
0.890
0.873
0.857
0.842
0.826
0.797
0.769
0.756
0.743
0.718
0.694
3
0.971
0.942
0.915
0.889
0.864
0.840
0.816
0.794
0.772
0.751
0.712
0.675
0.658
0.641
0.609
0.579
4
0.961
0.924
0.888
0.855
0.823
0.792
0.763
0.735
0.708
0.683
0.636...
Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15...
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Number of Aides Absent
5
8
11
15
4
2
7
1
4
6
14
19
3
5
8
In which of the following ranges you can find the Upper Control
Limit of the control chart?
0.1427
0.1536
0.1677
Not computable with information available
In which of the following ranges you can find the Lower Control
Limit of the control chart?
Does not exit...
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