STATISTICS II MEASURES OF DISPERSION Dispersion of a

STATISTICS (II) MEASURES OF DISPERSION

• Dispersion of a set of data is a measure of how the distribution is spread out

The measures include; • • • Range Interquartile Range Semi-Interquartile Range Mean Absolute Deviation Variance Standard Deviation or Root Mean Square Deviation

• Range Is the difference between the highest and the lowest values

• Interquartile Range The difference between the lower and the upper quartiles. It involves the middle 50% of the values

Semi-Interquartile Range or Quartile Deviation • Is half the Interquartile Range

Example: The end of term marks for a student in eight subjects is given below: 85, 32, 55, 87, 24, 78, 49, 38.

Determine the Range, Interquartile Range and the Semi-Interquartile Range of the data

Solution (a) Range: Arrange the data in order of increasing size 24, 32, 38, 49, 55, 78, 85, 87 Range=87 -24=63

(b) Interquatile Range 24, 32, 38, 49, 55, 78, 85, 87 Q 1 Q 2 Q 3= 78+85 = 81. 5, Q 1=32+38 = 35, 2 2 Q 3 -Q 1=81. 5 -35=46. 5

(c) Semi-Interquartile Range =½× 46. 5 =23. 25

Home Work Secondary Mathematics Students’ Book Four(Third Edition)-KLB Exer. 2. 3 No. 1(b)

For further reading visit the websites below: • https: //onlinecourses. science. psu. edu/stat 505/ node/18 • https: //www. mathsisfun. com/data/range. html