Question 1. How I construct frequency and relative distribution?

Question

using this table for Number of Arrivals at Wendy's: first column: 7, 5, 2, 6, 2, 6, 6, 4 second column: 6, 6, 7, 5, 2, 2, 8, 6 Third column: 6, 6, 1, 5, 9, 6, 2, 9 forth column: 6, 11, 2, 3, 7, 5, 6, 8 and fifth column: 4, 4, 4, 7, 5, 7, 5, 5

I am to construct a frequency and relative frequency distribution form the data.

The manager of Wendy's fast-food restaurant is interested in studying the typical number of customers who arrive during the lunch hour. The data in the table above represent the number of customers who arrive at Wendy's for 40 randomly selected 15-minute intervals of time during lunch. For, example, during the 15-minute interval, seven customers arrived. I am to Construct frequency and relative frequency distribution from the information. I need HELP!!

Answer 1

Hi Wanda,

The answer is actually much easier to find than you may think.

Recall that creating a frequency table simply involves creating a column for "x" ( the number of customers), and "n", representing the number of occurrences of each value of "x". So I would start like this:

x f

1 1

2 6

3 1

4 4

5 7

6 11

7 5

8 2

9 2

10 0

11 1

∑f = 40 = N

Now, at this point, you have a frequency table. Next you will want to calculate the relative frequencies, followed by the cumulative frequencies.

Before moving forward, you need a count of the sample size. You can obtain this in one of two ways: (a) add up the number of the x-values (NOT the values themselves), or (b) take a sum of the f column. Both of these approaches should provide you with the same answer. If they don't then you have made a calculation error.

(Note that "f" is the same as "n", meanining it refers to the sample size. N refers to the sum of n or f.)

As you can see the sum of n (or) f (and likewise, the total number of x-values) is 40.

To create a relative frequency distribution, simply divide each f value by N (the sum of n):

x p(x) Σ= f / N

1 1 / 40 = 0.025

2 6 / 40 = 0.150

3 1 / 40 = 0.025

4 4 / 40 = 0.100

5 7 / 40 = 0.175

6 11 / 40 = 0.275

7 5 / 40 = 0.125

8 2 / 40 = 0.050

9 2 / 40 = 0.050

10 0 / 40 = 0.000

11 1 / 40 = 0.025

Σ(p(x) = 1.000

Note that the sum of the probabilities should always add to 1.00. Otherwise you made a mistake in your calculations.

The final step is to create a cumulative frequency distribution. So far, you have already done all of the difficult work. The only additional piece of information that you need, is to cumulatively add the probabilities from one x-value to the next, as follows:

x cumulative frequency

1 0.025

2 0.150 + 0.025 = 0.175

3 0.025 + 0.175 = 0.200

4 0.100 + 0.200 = 0.300

5 0.175 + 0.300 = 0.475

6 0.275 + 0.475 = 0.750

7 0.125 + 0.750 = 0.875

8 0.050 + 0.875 = 0.925

9 0.050 + 0.925 = 0.975

10 0.000 + 0.975 = 0.975

11 0.025 + 0.975 = 1.000

And that's it. I hope this helps.

James