Question

What is an inetrquartile range?

Answer 1

if you have data :

1 2 3 4 5 6 7 8 9 10 11

lower quartile is 3

upper quartile is 9

Interquartile Range = 9 − 3 = 6

Interquartile Range is what you get when you

subtract the middle numbers

quartile has the word quart like quarter or 1/4

quartiles divide a list of numbers into three quarters

if you have

1 2 3 4 5 6 7 8 9 10 11

The middle quartile (or median), Q2, is the middle number in the set. It divides the set in two halves.

The lower quartile, Q1, is the middle number of the bottom half. It divides the bottom half in two.

The upper quartile, Q3, is the middle number of the top half. It divides the top half in two.

Subtract the lower quartile from the upper quartile = Interquartile Range

Interquartile Range = 9 − 3 = 6

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Answer 2

Explanation:

The interquartile range (IQR) is a measure of statistical dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) of a dataset. It is a measure of the spread or variability of the middle 50% of the data.

To calculate the interquartile range, you need to first arrange the dataset in ascending order. Then, find the median (Q2) of the entire dataset. Next, find the median of the lower half of the dataset, which is called the first quartile (Q1). Finally, find the median of the upper half of the dataset, which is called the third quartile (Q3).

The interquartile range is then calculated by subtracting Q1 from Q3: IQR = Q3 - Q1.

The IQR is useful because it provides a measure of the spread of the middle 50% of the data, which can help identify outliers or extreme values. It is less affected by extreme values compared to the range, making it a robust measure of dispersion.