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Chapter 6: Q 15. (page 369)

Benford鈥檚 law Exercise 9 described how the first digits of numbers in legitimate records often follow a model known as Benford鈥檚 law. Call the first digit of a randomly chosen legitimate record X for short. The probability distribution for X is shown here (note that a first digit can鈥檛 be 0). From Exercise 9, E(X)=3.441. Find the standard deviation of X. Interpret this value.

Short Answer

Expert verified

The standard deviation is 2.4618.

Step by step solution

01

Step 1. Given information.

The given information is:

02

Step 2. Find and interpret the standard deviation of X.

The given mean is 3.441.

The predicted value of the squared departure from the mean is known as the variance:

蟽2=鈭�x-渭2Px=1-3.4412脳0.301+2-3.4412脳0.176+3-3.4412脳0.125+4-3.4412脳0.097+5-3.4412脳0.079+6-3.4412脳0.067+7-3.4412脳0.058+8-3.4412脳0.051+9-3.4412脳0.046=6.060519

The standard deviation is:

蟽=蟽2=6.060519鈮�2.4618

We can see that on an average the first digit will vary from a mean of 3.441 by 2.4618.

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