Chapter 1. Tutorial: Measures of Center

1.1 Problem Statement

rand(0,9)
{22,24,29,27,21,23,25,26,20,29}
rand(0,9)
@v1[$vindex]
{27,21,20,22,24,29,23,25,28,30}
rand(0,9)
@v2[$vindex]
{23,22,25,21,26,27,20,24,29,28}
rand(0,9)
@v3[$vindex]
{58,44,52,54,50,58,50,48,60,54}
rand (0,9)
@v4[$vindex]
{28,20,26,23,25,24,21,22,30,27}
rand(0,9)
@v5[$vindex]
($v1+$v2+$v3+$v4+$v5)/5
($v1+$v2+$v3+$v5)/4
{27,22,26,23,25,27,23,25,29,29}
rand(0,9)
@dmed[$vindex]
$v4*2
{25,21.5,25.5,22.5,24.5,25.5,22,24.5,28.5,28.5}
@sortb[$vindex]
{23,21,25,22,24,24,23,24,28,28}
@sortc[$vindex]
{27,24,29,23,25,27,23,25,29,29}
@sortd[$vindex]
{27,22,26,23,25,27,23,25,29,29}
@sorte[$vindex]

How long does it take you to commute to school? Here are the travel times (minutes) measured from the time you leave your home to the time you arrive at your school for five days of commuting:

$v1, $v2, $v3, $v4*, $v5

On one of the days (marked with an asterisk), there was a traffic jam, and your commute was delayed.

1.2 Step 1

questions

One measure of the typical value is the sample mean.

Question 1.1

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Correct.
Incorrect.

Question 1.2

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Correct.
Incorrect.

Question 1.3

The single large outlier will 7jhHkwO9alYFz1x/oHVS4/PKnTh1d27HkR7ifbbUVE+yUXv/XA1ZTs5bTee6Hu5wvn+EDpjxR/C1GyVRjbrc5t1gmUnYKqlw8262QiiDfVnBkpakUciBUGLBlTxYrbD4mC0ge588OL+pO6u615toc1fkkF8=.

Correct.
Incorrect.

Question 1.4

Suppose that the starred value above was $doubleout minutes. Without doing any computations, the new mean computed with the revised values and all of the data would be 1hGinZ1HdYi0MLJVIFnzU9zqvrOulEEtitQsZI98xA9F5yGr6ZaPlqsMkd9PnR47jEptZgn0fzJMzgcywWhrhKo/YbMLkjP7yLPNIQ==.

Correct.
Incorrect.

1.3 Step 2

questions

Another measure of the typical value is the sample median.

Question 1.5

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Correct.
Incorrect.

Question 1.6

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Correct.
Incorrect.

Question 1.7

The single large outlier will 4GnFC+yumZtPGpO/HjE7bZWAiCi6myti2Ych4U1t00v0HVdXBFuI+wTAenTAtDRk9y8sxnduLqTABnaCv6JHzk5Pp/ap+0Ym3+QsdZXONUKyRbuyl1ay6IN3HA+XLJfUO1K8r0FX6GvM46oSFjbV+wc7uYhh60tg3H2/GZC4HD40vVmKBXZtUg==.

Correct.
Incorrect.

Question 1.8

Suppose that the starred value above was $doubleout minutes. Without doing any computations, the new median computed with the revised values and all of the data would be jiFHGf6LW22GyMQo7DLdJN1nH91reWErYdd/IhRbp0ql7qNztWGt7zpVM1Up2v35WNCg8Lb0uEqAssYLPcdBDnWnHtV0YmuNdcmUtPEFC8dzGfGuasD22w==.

Correct.
Incorrect.

1.4 Step 3

Suppose that on the day marked with an asterisk you forgot to record the exact time. All you know is that the commute time was larger than $v4 minutes.

questions

Question 1.9

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Correct.
Incorrect.

Question 1.10

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Correct.
Incorrect.

Question 1.11

In a roughly symmetric distribution, sCZdvpQlPVbnpHf8AKAnh2L4LJs1VKUlUCS7HYIxQCq2Cy+UpR1xZBqa0lxOlgWQrcm9Q40ASA3EUUl7qy6GDneq9ioUnClBYuREsv6Fft8MRtzY9gGwhyVNtxjVZqNYqU3cgIk0zIaZbMANrS0veQ1JqO1K+G8BrprzG2R9PGZLiQovwq+wJz8eJjIrbPNWvQvSPkU3E8gG1uex0GTh26GMdpD3RACO2fsv0FljzHa0D5yB.

Correct.
Incorrect.

Question 1.12

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Correct.
Incorrect.