bus-stat-book1

5 181 bowley s coefficient skewness q 3 q1 2 median q

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Unformatted text preview: f item 4 = Size of 39th item =5 Q2 Q3 N + 1 th = Median = Size of item 2 155 + 1 = Size of th item 2 = Size of 78th item =6 N + 1 th = Size of 3 item 4 155 + 1 th = Size of 3 item 4 = Size of 117th item = 6.5 181 Bowley’ s Coefficient Skewness = Q 3 + Q1 − 2 Median Q 3 − Q1 6.5 + 5 − 2 × 6 6.5 − 5 11.5 − 12 0.5 = = 1.5 1.5 = − 0.33 = Example 23: Calculate the value of the Bowley’ s coefficient of skewness from the following series. Wages : 10-20 20-30 (Rs) No.of Persons : 1 3 Solution: Wages(Rs) 10-20 20-30 30-40 40-50 50-60 60-70 70-80 30-40 40-50 50-60 60-70 70-80 11 21 43 32 9 F 1 3 11 21 43 32 9 N=120 N − m1 4 Q1 = l1 + × c1 f1 N 120 = = 30 4 4 Q1class = 40-50 l1= 40, m1=15, f1=21, c1=10 182 c.f 1 4 15 36 79 111 120 30 − 15 × 10 21 150 = 40 + 21 = 40 + 7.14 = 47.14 N −m 2 Q2 = Median = l + ×c f N 120 = = 60 2 2 ∴Q1 = 40 + Medianal class = 50 − 60 l= 50 , m=36, f = 43, c=10 60 − 36 median = 50 + × 10 43 240 = 50 + 43 = 50 + 5.58 = 55.58 N − m3 Q3 = l3 + 4 × c3 f3 N 120 3 = 3× = 90 4 4 Q3 class = 60 −70 l3=60, m3=79, f3=32, c3=10 90 − 79 ∴Q3 = 60 + × 10 32 110 = 60 + 32 = 60 +3.44 = 63.44 183 3 Bowley’ s Coefficient of skewness Q 3 + Q1 − 2 Median Q 3 − Q1 63.44 + 47.14 − 2 × 55.58 = 63.44 − 47.14 = 110.58 − 111.16 16.30 − 0.58 = 16.30 = − 0.0356 7.10.3 Measure of skewness based on moments: The measure of skewness based on moments is denoted by β1 and is given by: = If µ3 is negative, then β1 is negative 7.11 Kurtosis: The expression ‘ Kurtosis’ is used to describe the peakedness of a curve. The three measures – central tendency, dispersion and skewness describe the characteristics of frequency distributions. But these studies will not give us a clear picture of the characteristics of a distribution. As far as the measurement of shape is concerned, we have two characteristics – skewness which refers to asymmetry of a series and kurtosis which measures the peakedness of a normal curve. All the frequency curves expose different degrees of flatness or peakedness. This characteristic of...
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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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