Description
I.See attached chart
1. Determine the mean, median, mode, and range for the grade distribution of the Physics Test.
Mean:
Median:
Mode:
Range:
2. Determine the 5-Number summary and make a box-and-whiskers plot for the data. Include
the box-and-whiskers plot in your response.
3. What does the box-and-whiskers plot tell you about the shape of the distribution?
4. If John was the student who made a 71 on the test, which percentile did John score in?
5. Based on the interquartile range (IQR), does Professor Miller’s data set have any outliers? If
so, what is the outlier and why? Support your answer with your calculations.
6. Determine the variance and standard deviation of the data set.
7. Compare the mean and standard deviation of Professor Miller’s results on the 1st Physics test
to that of Professor Williams’, assuming that Professor Williams’ test had a mean of 84 and a
standard deviation of 5.6.
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Explanation & Answer
Dear Levi,Please find enclosed a doc file containing the step by step solution to the different statistics problems.
First of all, the easiest way to solve the different problems is by transforming the stem and leaf
plot into a table with the different grades:
19
46
47
53
55
55
56
60
65
66
68
69
70
70
70
70
70
71
73
73
73
74
74
75
75
76
77
77
78
78
78
78
79
79
79
80
80
81
82
82
83
83
83
85
86
86
86
87
88
88
88
89
89
89
90
90
90
90
91
91
92
93
93
93
93
93
93
95
95
96
96
96
98
100
100
1. Determine the mean, median, mode, and range for the grade distribution of the Physics
Test.
Mean:
𝑀𝑒𝑎𝑛 (𝜇) =
𝑆𝑢𝑚 𝑜𝑓 𝑠𝑐𝑜𝑟𝑒𝑠
5959
=
= 79.4
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑐𝑜𝑟𝑒𝑠
75
Median:
The median corresponds to the score located such that 50% of the scores lie below and 50% of
the scores lie above it. Since we have a total of 75 data, the median will be the score located in
the 38th position when scores are ordered from the lowest to the highest.
Taking this into account, the median of this set of data is 81.
Mode:
The mode corresponds to the score that appears with the highest frequency (that is, that is
repeated more times). Taking this into account, the mode of this set of data is 93, which i...
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