Copy of Copy of 9. Interpreting Standard Deviation GN
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Wagner College *
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Mathematics
Date
Jan 9, 2024
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docx
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Uploaded by ChancellorDanger13217
Name:
Date: 11/14/23
Period: 5
Aim: How do we interpret standard deviation?
Do Now:
Shown below are a few test scores from a math quiz out of 30, and the speeds of a few cars on a given highway in MPH. Without doing any calculations determine which one would have a higher standard deviation and explain your answer.
Test Scores: 5, 27, 13, 18, 30, 2, 7, Car Speeds: 65, 70, 63, 67, 70, 60, 65, 63
The car speeds would have a higher standard deviation because the numbers are greater.
Interpreting Standard Deviation
●
Standard deviation is a measure of the typical amount an entry deviates from the mean
●
The more the entries are spread out the greater the standard deviation.
Example
: For the previous problem, use your calculator to chalculate the standard deviation to the nearest
tenth and fill in the sentence starter below:
Test Scores: 5, 27, 13, 18, 30, 2, 7, Car Speeds: 65, 70, 63, 67, 70, 60, 65, 63
The test scores deviatesor differ from the mean on average by about 10.9 points.
The speeds are different from the mean by about 3.5
1)
The data set shows the hourly pay rates for all employees at a restaurant. Calculate mean and standard deviation of the data set to the nearest hundredth. $9.30, $8.20, $7.50, $8.50, $10.40, $9.30, $9.70, $9.30
Mean 9.02
Standard deviation .86
Summarize the data in a sentence:
There is a .86 difference between the peoples pay 2) Annual salaries (in thousands of dollars) for all electrical engineers at a company in Boston and a company in Chicago are listed. Boston: 60.4 64.1 58.5 64.5 65.6 59.9 68.3 170.1 69.9 Chicago: 69.4 71.5 75.4 69.9 70.9 68.5 72.9 70.1 70.9 (a) Using the calculator, find the mean and standard deviation of each data set to the nearest whole number.
Boston Mean 76000
Chicago Mean 71000
Boston Standard Deviation 34000
Chicago Standard Deviation 2000
(b) If you were an electrical engineer and wanted the best chance at a higher salary, which city would you pick to work in and why? Chicago because theres a lower difference between the salaries 3) Jake and Rudi are friends that play for different basketball teams.Their points scored across the first four games of the season are: Jake:
31,
35,
33
43 Rudi:
30,
67,
26,
25
Calculate their mean points scored and sample standard deviation rounded to the nearest whole
number.
Jake Mean 35.5
Rudi Mean 37
Jake Standard Deviation 4.6
Rudi Standard Deviation 17.42
Based on the average points scored per game Rudi argues he is better. Using standard deviation, explain who you think the best player is.
Jake is better because there's a smaller difference between the scores than rudis
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