## Calculate the Skewness and Kurtosis is values

Class Interval Frequency

20-30 18

30-40 35

40-50 65

50-60 32

60-70 10

Arithmetic mean= = 43.8125

Median = 40 +[ ] = 40+4.153846154

= 44.153846154

Mode = 40+ [ ] = 40 +

= 40+4.761904762 = 44.761904762

Q3 = 50 + = 50 +

= 50+0.625

=50.625

Q1= 30 + = 30+

= 30+6.285714286 = 36.288714286

Standard deviation = Ö = Ö 110.4647875

= 10.510223

 Class Interval Frequency (f) Mid class Value (x) xf Less than cumulative frequency x- ` x F(x- ` x) (x- ` x)2 F(x- ` x)2 (x- ` x)3 F(x- ` x)3 (x- ` x)4 F(x- ` x)4 20-30 18 25 450 18 -18.8125 -338.6250 353.9101 6370.3818 -6657.9348 -119842.8264 12525.3987 22545943.1770 30-40 35 35 1225 53 -8.8125 -308.4375 77.6601 2718.1035 -684.3801 -23953.3035 6031.0998 211088.4930 40-50 65 45 2925 118 1.1875 77.1875 1.4101 91.6565 1.6745 108.8425 1.9885 129.2525 50-60 32 55 1760 150 11.1875 358.0000 125.1601 4005.1232 1400.2292 44807.3344 15665.0647 501282.0704 60-70 10 65 650 160 21.1875 211.8750 448.9101 4489.1010 9511.2839 95112.8390 201520.3284 2015203.2840 Total 160 - 7010 - - 0 - 17674.3660 - 3767.1140 - 25273646.26

S f(x- ` x) 0

m 1 = ------------------ = ---------------------- = 0

160 160

S f(x- ` x)2 17674.3660

m 2 = ------------------ = ---------------------- = 110.4647875

160 160

S f(x- ` x)3 -3767.1140

m 3 = ------------------ = ---------------------- = -23.5444425

160 160

S f(x- ` x)4 25273646.26

m 4 = ------------------ = ---------------------- = 157960.2891

160 160

1) Karl-pearsons coefficient of Skewness for mode

Arithmetic mean-mode

Coefficient of Skewness = --------------------------------------

Standard deviation

43.8125-44.761904762

= -----------------------------------------

10.510223

= -0.00593377975

2) Karl-Pearson’s coefficient of skewness for median

3( Arithmetic mean-median)

Coefficient of Skewness = --------------------------------------

Standard deviation

3 (43.8125- 44.153846154)

= -----------------------------------------

10.510223

-1.02403845

= ------------------------------- = -0.097432609

10.510223

3) Bowley’s coefficient of skewness

Q3+Q1-2(median)

Bowley’s Coefficient of Skewness = --------------------------------------

Q3 - Q1

50.625+36.285714286- 2(44.153846154)

= -----------------------------------------

50.625 – 36.285714286

86.91071428 – 88.3076923

= -------------------------------------------

14.33928572

1.39697802

= ------------------------------- = - 0.97423124

14.33928572

4) Skewness from moments

m 3 2

Skewness ( b 1 ) = ---------------------

m 2 3

(-25.54444625)2

= -----------------------------------------

(110.4647875)3

652.5195644

= ------------------------------- = - 0.0004840853652

1347943.176

5) Kurtosis

m 4

Kurtosis( b 2 ) = ---------------------

m 2 2

157960.2891

= -----------------------------------------

(110.4647875)2

157960.2891

= ------------------------------- = 12.94494463

12202.46928