Quartile Ii

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Define quartile:
The word quartile comes from the word quarter, which means one fourth. It is a term used in statistics. For a set of data, the values that divide the entire set of observations into four equal parts are called quartiles. Therefore there would be 3 such points that divide the data set into 4 equal parts, so we have three quartiles - The first quartile, second quartile and the third quartile.

First quartile:
The first quartile is also known as the lower quartile. It is denoted by Q1. If a set of data has 19 observations, then the 5th observation would be the first quartile.

Second quartile:
The second quartile is also known as the median. It is denoted by Me. As above if the data set has 19 entries, then the 10th entry is the middle entry so that would be the median or the second quartile.

Third quartile:
The third quartile is also known as the upper quartile. It is denoted by Q3. If we consider the same set of data with 19 observations, then the third quartile would be the 15 observation.

If A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S are the ...
... 19 observations arranged in ascending order, then first quartile = E, second quartile = J and third quartile = O

We saw in the above example that for 19 number of observations the quartiles and the means are easily readable from the data set. That would be true for any number of observations that are not multiples of 4. However if the number of observations are multiples of 4, then the averages of the two median or quartile values are considered as quartiles or medians.

Inter quartile range:
The difference between first and the third quartile is called the inter quartile range. It is a measure of dispersion. Therefore inter quartile range = Qr = Q3 – Q1. So for the above example, Qr = O - E

Quartile deviation:
If Me is the value of the median, in a symmetric distribution
Me – Q1 = Q3 – Me. And this difference may be taken as the measure of dispersion. But as no distribution is rigidly symmetrical, it is usual to take the measure
Q = (Q3 - Q1)/2 and the Q is termed as quartile deviation, or better, the semi – inter quartile – range. It is not a measure of deviation from any particular average.
So for the above example, the quartile deviation = Q = (O-E)/2.

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