Variation in data sets

[Zelda22]

Question
Which of the samples shows more variation?

Sample 172,75,83,88,92,96,101,107,109,115,115,126,130

Sample 2
89,89,90,92,94,107,108,109,110,112,121

Answer:
I think is sample 1. But I wonder which is the best calculation I should use to answer?

I calculated,

Mean
Sample 1 Sample 2
102.2 101.9

MAD
Sample 1 Sample 2
15.5 10.1

IQR
Sample 1 Sample 2
27 20

Range
Sample 1 Sample 2
58 32

I think sample 1 has more variation because the data points are more spread. Is this correct? Thanks

 

[BigBeachBanana]

I would consider the pros and cons of each metric. Why would one be better than other?

 

[Zelda22]

I would consider the pros and cons of each metric. Why would one be better than other?

I'm not sure, that is exactly what I'm asking. I think the IQR?

 

[BigBeachBanana]

I'm not sure, that is exactly what I'm asking. I think the IQR?

Before I answer the question, just for my curiosity, are those metrics given to you as options, or it’s something you came up with?

 

[Zelda22]

Before I answer the question, just for my curiosity, are those metrics given to you as options, or it’s something you came up with?

I just trying to find a way to answer. I wasn't given any options.

 

[Zelda22]

I just realized a typo,

sample 1:

72,75,83,88,92,96,101,107,109,115,115, 122,126,130

sample 2:

89,89,90,92,94,107,108,109,110,112,121

 

[BigBeachBanana]

I just trying to find a way to answer. I wasn't given any options.

Ok, I thought so because MAD isn't common in practice and isn't usually taught in school anymore. It is more common to see the ordinary Variance. To answer your questions, IQR and range are useful, but they are also somewhat limited because they do not take into account every data point. Whereas, MAD takes into account every single data, and is more robust because it takes into consideration of the data's mean into account. The mean itself is a central tendency measure and not a dispersion measure. With that being said, by comparing the MADs, you're correct that data set 1 has a larger dispersion compared to data set 2.

 

[Zelda22]

Ok, I thought so because MAD isn't common in practice and isn't usually taught in school anymore. It is more common to see the ordinary Variance. To answer your questions, IQR and range are useful, but they are also somewhat limited because they do not take into account every data point. Whereas, MAD takes into account every single data, and is more robust because it takes into consideration of the data's mean into account. The mean itself is a central tendency measure and not a dispersion measure. With that being said, by comparing the MADs, you're correct that data set 1 has a larger dispersion compared to data set 2.

Thank you