bus-stat-book1

Weekly wage rs 100 200 400 500 600 no of weeks 5 8 21

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Unformatted text preview: 1 500 − 250 250 Q.D. = = = = 125 2 2 2 Q − Q1 Coefficient of Q.D. = 3 Q 3 + Q1 500 − 250 = 500 + 250 250 = = 0.3333 750 Position of Q1 in 146 Example 5: For the date given below, give the quartile deviation and coefficient of quartile deviation. X : 351 – 500 501 – 650 651 – 800 801–950 951–1100 f: 48 189 88 4 28 Solution : x 351- 500 501- 650 651- 800 801- 950 951- 1100 Total f 48 189 88 47 28 N = 400 True class Intervals 350.5- 500.5 500.5- 650.5 650.5- 800.5 800.5- 950.5 950.5- 1100.5 N − m1 Q1 = l1 + 4 × c1 f1 N 400 = = 100, 4 4 Q1 Class is 500.5 – 650.5 l1 = 500.5, m1 = 48, f1 = 189, c1 = 150 100 − 48 × 150 ∴ Q1 = 500.5 + 189 52 × 150 = 500.5 + 189 = 500.5 + 41.27 = 541.77 N 3 − m3 4 Q3 = l3 + × c3 f3 147 Cumulative frequency 48 237 325 372 400 N = 3 × 100 = 300, 4 Q3 Class is 650.5 – 800.5 l3 = 650.5, m3 = 237, f3 = 88, C3 = 150 300 - 237 × 150 ∴ Q3 = 650.5 + 88 63 × 150 = 650.5 + 88 = 650.5 + 107.39 = 757. 89 Q − Q1 ∴ Q.D = 3 2 757.89 − 541 .77 = 2 216.12 = 2 = 108.06 Q − Q1 Coefficient of Q.D = 3 Q 3 + Q1 757.89 − 541.77 = 757.89 + 541.77 216.12 = = 0.1663 1299.66 7.4.3 Merits and Demerits of Quartile Deviation Merits : 1. It is Simple to understand and easy to calculate 2. It is not affected by extreme values. 3. It can be calculated for data with open end classes also. Demerits: 1. It is not based on all the items. It is based on two positional values Q1 and Q3 and ignores the extreme 50% of the items 3 148 2. It is not amenable to further mathematical treatment. 3. It is affected by sampling fluctuations. 7.5 Mean Deviation and Coefficient of Mean Deviation: 7.5.1 Mean Deviation: The range and quartile deviation are not based on all observations. They are positional measures of dispersion. They do not show any scatter of the observations from an average. The mean deviation is measure of dispersion based on all items in a distribution. Definition: Mean deviation is the arithmetic mean of the deviations of a seri...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.

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