Project 7 Math Part 1 (1)
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Course
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Subject
Mathematics
Date
Jan 9, 2024
Type
docx
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Uploaded by MateScienceFerret44
Project 7 for MATH 269
Group 7
Md Saeid Hasan Emon
301268164
Mohammad Fahim Hasan
301288856
Mazharul Islam Uchhwas
301277629
Submitted to: Darshana Patel
Date of submission: October 30
th
, 2023
The response times of a sample of 55 LCD monitors have been collected to evaluate whether the manufacturer's claim of reducing response time to less than 2.34ms holds true. The following analysis explores various descriptive statistics to gain insights into the data.
i) Rearranging data from lowest to highest
ii) Mean, median, mode, range, midrange
Mean:
1.31
1.54
1.59
1.64
1.68
1.70
1.70
1.71
1.73
1.74
1.74
1.77
1.80
1.82
1.84
1.84
1.86
1.88
1.89
1.89
1.89
1.93
1.93
1.94
1.94
1.94
1.95
1.95
1.98
1.99
2.00
2.01
2.01
2.03
2.04
2.07
2.09
2.09
2.13
2.14
2.15
2.16
2.16
2.17
2.18
2.19
2.20
2.23
2.23
2.24
2.24
2.28
2.3
2.33
2.57
Mean = 1.31
+
1.54
+
⋯
+
2.33
+
2.57
55
= 108.35
55
= 1.97
The mean response time for the given LCD monitors is approximately 1.97 milliseconds.
Median:
Since there are 55 observations, an odd number, the median is the middle value when the data is sorted. The median is the value at the center, which is the average of the two middle values.
median is the value at position p where
P
=
n
+
1
2
= 55
+
1
2
= 28
From rearranging the numbers,
1.31, 1.54, 1.59, 1.64, 1.68, 1.7, 1.7, 1.71, 1.73, 1.74, 1.74, 1.77, 1.8, 1.82, 1.84, 1.84, 1.86, 1.88, 1.89, 1.89, 1.89, 1.93, 1.93, 1.94, 1.94, 1.94, 1.95, 1.95, 1.98, 1.99, 2, 2.01, 2.01, 2.03, 2.04, 2.07,
2.09, 2.09, 2.13, 2.14, 2.15, 2.16, 2.16, 2.17, 2.18, 2.19, 2.2, 2.23, 2.23, 2.24, 2.24, 2.28, 2.3, 2.33, 2.57
Therefore, the median response time for the LCD monitors is 1.95 milliseconds.
Mode:
The mode of the response times is 1.89 & 1.94 milliseconds, as it appears more frequently than any other value.
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Range:
Range = Maximum value − Minimum value
Range = 2.57 − 1.31
Range = 1.26
The range of response times is 1.26 milliseconds.
Midrange:
Midrange= Max mum
ⅈ
value
−
minimumvalue
2
= 2.57
+
1.31
2
= 1.94
The midrange of the response times is 1.94 milliseconds.
iii) Standard deviation and variance
Mean, ~
x
= 1.97
Now, Variance, s
2
= Σ
(
ϰ
−
~
x
)
2
n
−
1
, s
2
= (
1.31
−
1.97
)
2
+
…
⋅
+
(
2.57
−
1.97
)
2
55
−
1
s
2
= 0.53296
And, Standard Deviation, S = √
S
2
= √
0.53296
=0.23085
iv) percentile for any two values of x, and P
38
∧
P
60
Location of, P
38
= 38
100
(
55
+
1
)
= 21.28
The percentile will be the average of the values positioned in the 21 and 22
Position. The average of the 21th and 22th items represent the 38th percentile (
P
38
).
Therefore,
P
38
= 1.89
+
1.93
2
= 1.91
And, Location of, P
60
= 60
100
(
55
+
1
)
= 33.6
The percentile will be the average of the values positioned in the 33 and 34
Position. The average of the 33rd and 34th items represent the 60th percentile (
P
60
).
Therefore,
P
60
= 2.01
+
2.03
2
= 2.02
vi) frequency table and histogram
Value
Frequency
1.31
1
1.54
1
1.59
1
1.64
1
1.68
1
1.70
2
1.71
1
1.73
1
1.74
2
1.77
1
1.80
1
1.82
1
1.84
2
1.86
1
1.88
1
1.89
3
1.93
2
1.94
3
1.95
2
1.98
1
1.99
1
2.00
1
2.01
2
2.03
1
2.04
1
2.07
1
2.09
2
2.13
1
2.14
1
2.15
1
2.16
2
2.17
1
2.18
1
2.19
1
2.20
1
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2.23
2
2.24
2
2.28
1
2.30
1
2.33
1
2.57
1
Frequency Table. VALUE RANGE
Frequency
1.30-1.49
1
1.50-1.69
4
1.70-1.89
16
1.90-2.09
17
2.10-2.29
14
2.30-2.49
2
2.50-2.69
1
vii) Construct a boxplot – include calculations for Q1
Q3
∧
The Quartile formula for Q1
= 1
4
(
?
+
1
)
h
?
= 1
4
(
55
+
1
)
h
?
= 14
h
?
From r
earranged data list, 14
th
value is = 1.82
The Quartile formula for Q3
= 3
4
(
?
+
1
)
h
?
= 3
4
(
55
+
1
)
h
?
= 42
??
From r
earranged data list,42nd value is = 2.16