The goal of this homework is to give you the opportunity to show me you can do s

Question

The goal of this homework is to give you the opportunity to show me you can do some work with “Google sheets”

Beneford’s law describes the probability of a leading digit being 1, 2, 3, 4, …,9 Those probabilities are graphed below.

From Wikipedia: Benford’s law applies:

“… to a wide variety of figures, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws.” Benford’s law is also used in detecting tax fraud among other things.

The graph of the probabilities is below:

Figure 1

A) Begin by entering the numbers 1 through 9 into google sheets.

               Figure 2

B) Calculate the probabilities by using the formula below, then copy, and paste the formula into the remaining digits to get all probabilities. The formula is , where the “Log” is in base ten. Type in the formula as shown in the circle of figure 3.

Copy the formula all the way to the bottom using “Control C” to copy, and “Control V” to paste. (“Command C” and “Command V” on a Mac)

Figure 3

C) Create the entries in column “C” as the product of columns A and B, as in figure 4 below. The command to use is circled in red. Use the sum of column C to find the expected value (= mean = m). Next, calculate the variance by finding the value of . Create the numbers in column “D” by Each term in this sum can be calculated as in figure 5. Note that the value 3.440236 is the mean calculated from the sum of the previous column.

Figure 4 (top)   

  Figure 5 (bottom)

D) Find the sum of column “D” to get the variance, then find the “standard deviation”. Use the table to answer the following questions.

1) Do the probabilities graphed in figure 1 have a “Normal Shape”, “Uniform shape”, or “Other”      ____________

(See page 56 in your book)

2) List the mean _____________ Variance _____________ and Standard Deviation _____________   for this data set.

3) What are the “typical values” for this distribution according to the “range rule of thumb” on page 202?

4). Use your distribution, the “=Sum(” command from Google sheets, and the complementation rule to find the following probabilities:

a)                                           b)

c                                        d)

5) Feedback. Was this assignment easy? Hard? Do you like using “Google sheets” to do this as opposed to a graphing calculator? (Note: I’m not looking for “suck-up” answers, I’m looking for your honest opinion, I want to know if you think learning stats using google sheets is a good thing or not)

6) Copy your work on google sheets and the answer to questions 1-5 into a google doc or a MS Word file using Grab for Macs or the snipping tool for Windows. Save your file on the desktop or other place where you have easy access to it.

Explanation / Answer

The probability has “Other” shape Mean = 5, Variance = 8.49 , std Dev = 2.9 Range = maximum – minimun = 8

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.