Interquartile range

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Dina statistik deskriptif, the interquartile range (IQR) is the difference between the third and first quartiles. The interquartile range is a more stable statistic than the range, and is usually preferred to that statistic.

Since 25% of the data are less than or equal to the first quartile and 25% are greater than or equal to the third quartile, the difference is the length of an interval that includes about half of the data. This difference should be measured in the same units as the data.

[édit] Percentiles and quartiles

For a sample of $n$ observations $x 1, x 2,.... x n$ the observations are ordered from small to large. From these order statistics you can find the sample percentiles.

If $0 < p < 1$ , the 100 $p$ th sample percentile has approximately $n p$ sample observations smaller less than it and also $(n + 1) p$ sample observations greater than it. One way of achieving this is to take the (100 $p$ )th sample percentile as the $(n + 1) p$ order statisic, provided that $(n + 1) p$ is an integer.

If $(n + 1) p$ is not an integer but is equal to $r$ plus some fraction $a / b$ then you can use a linear interpolation between $y r$ and $y r + 1$ . So the 100 $p$ th sample percentile is defined as:

$\tilde{\pi}_p = y_r +(a/b)(y_{r+1}-y_r)$

Certain percentiles have special names. The 50th percentile is the median of the sample. The 25th, 50th, and 75th percentiles are the first, second and third quartiles of the sample. This gives us five-number summary of a set of data. Its constituents are: minimum, the first quartile, the median, the third quartile and the maximum. Written is this order.

Now the IQR or interquartile range is defined as:

$IQR = \tilde{r}_3-\tilde{r}_1.$

[édit] Conto

Itungan ieu make data tina kaca quartile.

     i    x[i]
     1    102
     2    105
    ----------- the first quartile, Q[1] = (105+106)/2 = 105.5
     3    106
     4    109
   ------------ the second quartile, Q[2] or median = 109.5
     5    110
     6    112
   ------------ the third quartile, Q[3] = (112+115)/2 = 113.5
     7    115
     8    118

Tina tabel eta, the interquartile range is 113.5 - 105.5 = 8

Tempo ogé: statistical dispersion, mean

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Interquartile range

Ti Wikipédia, énsiklopédi bébas

[édit] Percentiles and quartiles

[édit] Conto

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