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## Calculate Kurtosis and Skewness from the given data in Excel.

 Range f 0-10 1 10-20 7 20-30 14 30-40 7 40-50 1

### Formula Recalling:

Kurtosis = (Quartile Deviation)/(P90 -P10)=(Q3 -Q1)/2(P90-P10)

Skewness =(Mean -Mode)/Standard deviation (σ)

### Step 1

Calculating quatile 1 (Q1), quartile 3 (Q3), P10, P90, Mean, Mode, and Standard Deviation

Quartile 1 and Quartile 3

 Quartile 1 Q1 item 7.5 =(D17/4) Q1 class 10-20 Q1 19.286 =B13+(B20-F12)/D13*(C13-B13) Quartile 3 Q3 item 22.5 Q3 class 30-40 Q3 30.714 =B15+(B25-F14)/D15*(C15-B15)

Source: Excel 2013

Percentile 10 and Percentile 90

 Percentile 10 P10 item 3 P10 class 10-20 P10 12.86 =B13+(E20-F12)/D13*(C13-B13) Percentile 90 P90 item 27 P90 class 30-40 P90 37.14 =B15+(E25-F14)/D15*(C15-B15)

Source: Excel 2013

Mean, Standard Deviation, and Mode

Model calculation

 Model Class 20-30 [Highest frequency class] Mode 25 =L+((f(1)-f(0))/(2*f(1)-f(0)-f(2)))*(C14-B14)

Source: Excel 2013

 Mean 25 SD 8.5635

To know the calculation procedure of mean and standard deviation, click here.

### Step 2

Calculating Kurtosis

 Kurtosis 0.2353 =(Q3-Q1)/(2*(P90-P10))

Source: Excel 2013

Calculating Skewness

 Sk =(Mean-Mode)/Standard Deviation

Source: Excel 2013

### Conclusion

we follow two steps in calculating skewness and kurtosis.

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