Question

Finding the three measures of dispersion, then plotting a frequency polygon.

5. Given the following frequency distribution, find the three measures of dispersion. When you are finished, plot a frequency polygon from these data and mark off the mean in s units. Rounds to a whole number for ease of plotting,

Answer 1

Three measures of dispersion : Range, interquartile range, and standard deviation

Range
Lowest value in x with frequency > 0 = 1
Highest value in x with frequency > 0 = 9
Range = 9-1 = 8

Interquartile range :

1st arrange data in to ascending order then find the cumulative frequency as follows

cf: cumulative frequency

Solution: Frequency 1 1 1 3 | 1 AO V 00vw w - - 23 30 36 40 --- n = 40

Here, n = 40 Q=(.*2 )" value of the observation n + 1 )th value of the observation value of the observation = (10.25)th value of the observation = 5 (3(n + 1) lth value of the observation Q3 = (36 * 1)" value of the observation = (341)" value of the observation 3:41th value of the observation = (30.75)th value of the observation = 8

Interquartile range = Q3 - Q1 = 8 - 5 = 3

Standard deviation :

Solution: x Frequency (f) fix = (2) (1) f:x2 = (f:x) x (x) (4) = (3) (1) (2) 36 324 8 6 48 384 49 Tot 343 288 8 8 48 5 7 7 35 175 - 12 9 3 27 1 --- n = 40 {f.x = 240 {f. x2 = 1594 TY Mean x = 240 40 = 6

Ef:x2 (Ef.x)2 п Population Standard deviation o = 1 Population Standard deviation o = /25•2. CENE (240) 2 40 40 1594 - 1440 40 154 40 = 13.85 = 1.9621

Standard deviation = 1.9621

Frequency ploygon :

or 1 2 3 4 5 6 7 8 9 10

PL??