Math 3770T, Exam 1 Solutions
Problem 1.
At a certain meteorological station temperatures are taken during a two weeks
period and the outcomes are
70
,
73
,
80
,
83
,
99
,
77
,
70
,
63
,
69
,
73
,
82
,
60
,
64
,
77
.
1. Find the mean and the median.
2. Draw a histogram of the sample and the density based on the temperature intervals
[60
,
70)
,
[70
,
75)
,
[75
,
82)
,
[82
,
100)
.
3. Drop the lowest and the highest temperatures from the sample and ﬁnd the mean and
the median of the remaining sample. Is there any change from the full sample? How
about the mean? Explain.
Solution.
1.
Mean
= 74
.
28
,
Median
= 73
.
2. Here are the pictures. The ﬁrst one is the histogram and the other one is the density.
70
80
90
100
0.5
1.0
1.5
2.0
70
80
90
100
0.01
0.02
0.03
0.04
0.05
0.06
3.
Mean
= 73
.
41
,
Median
= 73
.
The mean decreases a bit because the highest values is 99 while the lowest is 60. The
mean thus decreases as the distance from 99 is higher than the distance from 63 to the
original mean 74. The moral is that 99 contributes more to the original average as 60
does.
The median stays the same as we just eliminate the smallest and the largest, thus the
midvalues is still the same.
Problem 2.