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Remi.b
Remi.b
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The red bracket represents the smallest interval that encompass 50% of the data.

The two quartiles represents the first 25% of the data from each side of the mean encompassing for 50% of the data but this is not necessarily the densest region. The densest region does not even need to include the the median.

Imagine a skewed distribution that has a very long tail on the right. The median might be much higher than the mode and be fairly high. In consequence the 25% quartile will eventually include the mode but the right quartile will be long in a very sparse space. The densest region necessarily include the median (exception in @whuber's comment below) and one of the two quartile.

The red bracket represents the smallest interval that encompass 50% of the data.

The two quartiles represents the first 25% of the data from each side of the mean encompassing for 50% of the data but this is not necessarily the densest region. The densest region does not even need to include the the median.

Imagine a skewed distribution that has a very long tail on the right. The median might be much higher than the mode and be fairly high. In consequence the 25% quartile will eventually include the mode but the right quartile will be long in a very sparse space.

The red bracket represents the smallest interval that encompass 50% of the data.

The two quartiles represents the first 25% of the data from each side of the mean encompassing for 50% of the data but this is not necessarily the densest region.

Imagine a skewed distribution that has a very long tail on the right. The median might be much higher than the mode and be fairly high. In consequence the 25% quartile will eventually include the mode but the right quartile will be long in a very sparse space. The densest region necessarily include the median (exception in @whuber's comment below) and one of the two quartile.

Source Link
Remi.b
Remi.b
  • 5.2k
  • 12
  • 43
  • 72

The red bracket represents the smallest interval that encompass 50% of the data.

The two quartiles represents the first 25% of the data from each side of the mean encompassing for 50% of the data but this is not necessarily the densest region. The densest region does not even need to include the the median.

Imagine a skewed distribution that has a very long tail on the right. The median might be much higher than the mode and be fairly high. In consequence the 25% quartile will eventually include the mode but the right quartile will be long in a very sparse space.