Interquartile

If the number of values of ranked data is divided into four equal parts, then the lines marking each division are quartiles. The interquartile range is the difference between the values of the upper and lower quartiles. The closer the clustering of values around the median , the smaller the interquartile range. The value of the interquartile range is important when two sets of similar data are compared.

The distance between the top of the lower quartile and the bottom of the upper quartile of a distribution is defined as interquartile.

The interquartile range is a measure of variability, spread or dispersion. It is the difference between the 75^th percentile (often called Q₃) and the 25^th percentile (Q₁).

The formula for interquartile range is therefore: Q₃ - Q₁. It is sometimes called the H- spread.

Since half the scores in a distribution lie between Q₃ and Q₁, the semi-interquartile range is 1/2 the distance needed to cover 1/2 the scores. In a symmetric distribution, an interval stretching from one semi-interquartile range below the median to one semi-interquartile above the median will contain 1/2 of the scores.

Example:-

Step 1: Put the numbers in order

1,2,5,6,7,9,12,15,18,19,27

Step 2: Find the median

1,2,5,6,7,9,12,15,18,19,27

Step 3: Place parentheses around the numbers above and below the median. Not necessary statistically but it makes Q₁ and Q₃ easier to spot.

(1,2,5,6,7),9,(12,15,18,19,27)

Step 4: Find Q₁ and Q₃ Q1 can be thought of as a median in the lower half of the data, and Q₃ can be thought of as a median for the upper half of data.

(1,2,5,6,7), 9, ( 12,15,18,19,27). Q₁ =5 and Q₃ =18.

For a grouped frequency distribution, cumulative frequencies (less than type) are to be calculated first. Then

Q₁ =the value that corresponds to cumulative frequency N/4

Q₃ =the value that corresponds to cumulative frequency 3N/4