Will give medal. The box plots show attendance at a local movie theater and high school basketball games:
Which of the following best describes how to measure the spread of the data?

- anonymous

- chestercat

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- anonymous

The IQR is a better measure of spread for movies than it is for basketball games.
The standard deviation is a better measure of spread for movies than it is for basketball games.
The IQR is the best measurement of spread for games and movies.
The standard deviation is the best measurement of spread for games and movies.

- anonymous

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- anonymous

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- anonymous

- anonymous

1 think its either A or C.

- anonymous

still working it out? @mathmate

- mathmate

@bloofoffiction
Have you done all the common measures of spread, including
Range, IQR, absolute deviation, variance and standard deviation?

- anonymous

1've doen the IQR

- mathmate

and the range and standard deviation?

- anonymous

what do you mean by range?

- mathmate

The question compares IQR and the standard deviation, so it is evident that it's part of your course!

- anonymous

you can't actually calculate anything because there is no data chart

- mathmate

range is the difference between the largest and the smallest values.

- mathmate

This question is a qualitative one, so no calculator required. Its checks the understanding of the applicability of each measure, not actually calculating it.

- anonymous

theres no actual number 1 can guess

- mathmate

In each box and whisker plot, you see the five values in each, right? (the minimum, Q1, Q2(median), Q3 and the maximum).

- anonymous

yes

- mathmate

Do you know the significance/meaning of these values?

- anonymous

yes

- mathmate

So these values divide the dataset into 4 equal parts, right?
If there are 100 observations in the dataset, the number of observations between each sequential values contains 25 observations, ok so far?

- anonymous

yes

- mathmate

Can you tell me the possible reasons why the maximum for movies is so far to the right, or why the minimum for basketball is so far to the left?

- anonymous

outliers

- mathmate

exactly!
Is the IQR affected by the outliers?

- anonymous

yes

- mathmate

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- mathmate

From the diagrams of both cases with or without outliers, we see that the IQR is hardly affected, if any, right?

- anonymous

yes

- anonymous

so if there are outliers IQR should be used and if there aren't standard deviation should be?

- mathmate

Yes, more or less.
We will also give some kind words for standard deviation!
Standard deviation takes into account of ALL data points in the dataset.
The only problem is that standard deviation squares the difference between data values and the mean, so it is highly affected by outliers.
It is a much better measure for a properly distributed dataset.

- anonymous

so it should be C?

- mathmate

I do not know what C says.
But if you consider the datasets, there is a possibility that we are dealing with outliers (although we cannot be sure). In such cases, I would recommend the IQR.
For more detailed discussions, I suggest you do some interesting reading such as the following:
https://statistics.laerd.com/statistical-guides/measures-of-spread-absolute-deviation-variance.php
Btw, if you repeat what your suggested answer is (not just the letter, but the value of the answer), I will be glad to confirm it.

- anonymous

The IQR is the best measurement of spread for games and movies.

- mathmate

I agree!

- anonymous

can you help with one more?

- mathmate

I'm sorry, I have the next appointment. But if you post your question, and it's not answered when I finish, I'll be there! Nice working with you!

- anonymous

okay thanks!

- mathmate

You're welcome! :)

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