KIN 206 Assignment 1 - Natasha Witts 43703610
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University of British Columbia *
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Course
206
Subject
Health Science
Date
Dec 6, 2023
Type
docx
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Uploaded by MasterCamel3815
Assignment 1
Natasha Witts (43703610)
School of Kinesiology, University of British Columbia
KIN 206: Introduction to Statistics in Kinesiology
Dr. Carolyn McEwen
October 6
th
, 2023
Step 1
a) Unadjusted Table
Frequencies for Sitting
Sitting Frequency Percent
Valid
Percent
Cumulative
Percent
1
1
0.74
0.74
0.74
2
2
1.47
1.47
2.21
3
3
2.21
2.21
4.41
4
3
2.21
2.21
6.62
5
15
11.03
11.03
17.65
6
24
17.65
17.65
35.29
7
25
18.38
18.38
53.68
8
24
17.65
17.65
71.32
9
14
10.29
10.29
81.62
10
9
6.62
6.62
88.24
11
4
2.94
2.94
91.18
12
8
5.88
5.88
97.06
13
1
0.74
0.74
97.79
14
1
0.74
0.74
98.53
15
1
0.74
0.74
99.26
44
1
0.74
0.74
100.00
Missin
g
0
0.00
Total
136
100.00
b) There was problematic data in the assignment data provided. The problem was with one of the
values for the hours spent sitting during a day, a 24-hour period, with that value being 44 hours
spent sitting. The poll conducted collected the number of hours within a 24-hour period that
students were sitting, so a value of 44 would surpass the 24-hour window making the data
problematic. The problematic data can be adjusted by the removal of the value.
Adjusted Table
Frequencies for Hours Spent Sitting
Sitting
FrequencyPercent Valid Percent Cumulative Percent
1
1
0.74
0.74
0.74
2
2
1.47
1.48
2.22
3
3
2.21
2.22
4.44
4
3
2.21
2.22
6.67
5
15
11.03
11.11
17.78
Frequencies for Hours Spent Sitting
Sitting
FrequencyPercent Valid Percent Cumulative Percent
6
24
17.65
17.78
35.56
7
25
18.38
18.52
54.07
8
24
17.65
17.78
71.85
9
14
10.29
10.37
82.22
10
9
6.62
6.67
88.89
11
4
2.94
2.96
91.85
12
8
5.88
5.93
97.78
13
1
0.74
0.74
98.52
14
1
0.74
0.74
99.26
15
1
0.74
0.74
100.00
Missing
1
0.74
Total
136
100.00
Step 2
Descriptive Statistics
Sitting
Valid
135
Missing
1
Mode
6.99
Median
7.00
Mean
7.48
Std. Deviation
2.42
Variance
5.88
Skewness
0.36
Std. Error of
Skewness
0.21
Kurtosis
0.60
Std. Error of Kurtosis
0.41
Range
14.00
Minimum
1.00
Maximum
15.00
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Hours Spent Sitting
a)
The distribution is unimodal with only one peak being prevalent and there is also a slight
positive skew. There is a positive statistic that indicates the positive skew, however the
mean is greater than the median which is indicative of a positive skew as well. The
histogram as well as kurtosis also indicate that there is more of a leptokurtic distribution
with there being less variability within the data.
b)
The measure of central tendency that would represent the distribution the best for this
data would be the median. With the leptokurtic distribution, the median would best
represent this distribution as there is not a large amount of variance within the data so it
can help provide a more accurate representation. The median also tends to be quite an
accurate measure of central tendency when it comes to having a distribution that is
skewed.
Step 3
Hours Spent Sitting
The bottom edge of the box represents the 25
th
percentile, or first quartile, and this means that
25% of the students spent 6 hours sitting per day or less. The line in the middle of the box
represents the 50
th
percentile, sitting at the 7 hours which is the median, with 50% of students
being at or below that many sitting hours per day. The upper edge of the box represents the 75
th
percentile, or third quartile, showing that 75% of the students sat for roughly 9 hours per day.
The whiskers of the box-plot show the minimum and maximum, with a few outliers that skew
the box-plot.
Step 4
Z
=
X
−
μ
σ
Z
=
12
−
7.48
2.42
Z
=
1.87
Standardized Data for Hours Spent Sitting
Hours
Sitting
Standardized
Frequency
1
-2.68
1
2
-2.26
2
3
-1.85
3
4
-1.44
3
5
-1.02
15
6
-0.61
24
7
-0.2
25
8
0.21
24
9
0.63
14
10
1.04
9
11
1.45
4
12
1.87
8
13
2.28
1
14
2.69
1
15
3.11
1
The collected data was only relevant to the class population and was not used as a sample from a
larger population to determine how many hours they spent sitting on a Tuesday. For this reason,
population values, such as the population mean of 7.48 and population standard deviation of
2.42, can be used as they are known values.
Step 5
The shape of the distribution did not change because it is a linear transformation, however after
converting the scores to a standard score there was a change in how JASP formatted the
distribution in the histogram. Instead of the values going from the most negative of -2.68 to the
most positive of 3.11, they went from least negative to most negative, back to zero and then from
least positive to most positive. This gave the illusion of the distribution shape changing when it
was only the formatting of the distribution that had been changed.
Step 6
X
=
Mean
+(
Z ×Standard Deviation
)
X
=
7.48
+(
Z×
2.42
)
For -2:
X
=
7.48
+(
Z×
2.42
)
X
=
7.48
+(−
2
×
2.42
)
X
=
7.48
−
4.84
X
=
2.64
hours
Z-Score of -2 corresponds to 2.64 hours
For -1
X
=
7.48
+(
Z×
2.42
)
X
=
7.48
+(−
1
×
2.42
)
X
=
7.48
−
2.42
X
=
5.06
hours
Z-Score of -1 corresponds to 5.06 hours
For 0
X
=
7.48
+(
Z×
2.42
)
X
=
7.48
+(
0
×
2.42
)
X
=
7.48
+
0
X
=
7.48
hours
Z-Score of 0 corresponds to 7.48 hours
For 1
X
=
7.48
+(
Z×
2.42
)
X
=
7.48
+(
1
×
2.42
)
X
=
7.48
+
2.42
X
=
9.90
hours
Z-Score of 1 corresponds to 9.90 hours
For 2
X
=
7.48
+(
Z×
2.42
)
X
=
7.48
+(
2
×
2.42
)
X
=
7.48
+
4.84
X
=
12.32
hours
Z-Score of 2 corresponds to 12.32 hours
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Step 7
% sitting between 8 to 12 hours per day = 17.65% + 10.29% + 6.62% + 2.94% + 5.88%
% sitting between 8 to 12 hours per day =
43.38%
Hours
Sitting
Frequenc
y
8
9
10
11
12
Total
Around 59 of the students who reported, so 43.38% of the students, spend 8 to 12 hours per day
sitting.