midterm1+sol

# midterm1+sol - Math 3770T Exam 1 Solutions Problem 1 At a...

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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.

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## This note was uploaded on 05/26/2010 for the course ECE 3025 taught by Professor Citrin during the Spring '08 term at Georgia Tech.

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midterm1+sol - Math 3770T Exam 1 Solutions Problem 1 At a...

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