Question 1199741: The highway mileage (mpg) for a sample of 9 different models of a car company can be found below.
43 31 37 44 50 40 39 25 50
Click to Copy-and-Paste Data
Data: 43,31,37,44,50,40,39,25,50
Find the mode:
Find the midrange:
Find the range:
Estimate the standard deviation using the range rule of thumb:
Now use technology, find the standard deviation:
(Please round your answer to 2 decimal places)
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Answers:
Mode = 50
Midrange = 37.5
Range = 25
Standard Deviation Estimate = 6.25
Standard Deviation More Accurate Value = 8.22
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Explanation:
Let's start off by sorting the values from smallest to largest.
43,31,37,44,50,40,39,25,50
sorts to
25,31,37,39,40,43,44,50,50
You can sort by hand, or use technology to do so.
The most frequent value is 50 since it shows up twice, whereas everything else shows up exactly once.
This is why the mode is 50.
Side note: multiple modes are possible. It's also possible to not have any mode at all.
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Refer to the sorted set to find
min = smallest value = 25
max = largest value = 50
Then,
midrange = (min+max)/2
midrange = (25+50)/2
midrange = (75)/2
midrange = 37.5
The midrange is the midpoint of the smallest and largest items.
It's a measure of center, but it doesn't get used very much.
Despite the fact the word "range" is part of the word "midrange", the midrange is not a measure of spread. This can be slightly confusing for students.
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Range = max - min
Range = 50 - 25
Range = 25
This is a measure of how spread out the data set is.
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The range rule of thumb is where we divide the range over 4 to get an estimate of the standard deviation
range/4 = 25/4 = 6.25
Further Reading:
https://www.statology.org/range-rule-of-thumb/
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When it comes to technology, it's up to you which tool you prefer.
There are many options to pick from.
Here's one free online calculator
https://www.calculator.net/standard-deviation-calculator.html
Be sure you go for sample standard deviation, and not population standard deviation.
They're slightly different concepts.
A sample standard deviation is used because this given data set is a sample.
Use technology to determine the sample standard deviation is roughly 8.22
This isn't really that close to 6.25 we estimated earlier, but I suppose it could be worse.
The standard deviation is also a measure of spread. This is why the range rule of thumb is somewhat loosely connected to the standard deviation.
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