# Section 6.2 Question 4

### What is the mode of a dataset?

The mode of a dataset is the value that occurs most frequently in the data. In the dataset for the time it takes a customer to make a deposit, we were given the data below. The original data was shown in a table,

and used to create a frequency table.

The time of 3 minutes occurs seven times and is the most frequently occurring data value. Therefore the mode of this data is 3. Note that the mode is a data value and not the frequency associated with that value.

### Example 6      Mode of Home Sales

During the week of 6/7/2012 through 6/14/2012, eight homes were sold in Paradise Valley, Arizona in the area code 85253. The sales prices for these homes are listed below.

900,000      535,000      182,500      1,550,000      2,250,000      1,525,000      490,000      1,525,000

Find the mode of the home sales prices.

Solution The home sale price of 1,525,000 occurs twice compared to all other prices occurring once. The mode is 1,525,000.

If a dataset has two values that occur most frequently, the data is said two have two modes. In this situation, we must make sure the mode is quoted as the two data values and not the frequency.

### Example 7      Find the Mode

A used clothing retailer needs to insure that she has ample stock of dress sizes most commonly purchased by her customers. To do this, she offers a bounty of dress sizes that are in high demand. She surveys 16 customers and asks them what their dress size is.

12      6      14      18      10      14      8      10
16      16      20      16      16      14      14     8

a.   Find the mode of this dataset.

Solution To help determine which value occurs most frequently, construct a frequency table.

Sizes 14 and 16 occur most frequently with four occurrences each. The data has two modes at 14 and 16. She should offer top dollar to customers who wish to sell these sizes since she sells those sizes most frequently.

b.   Why is the mode a better choice for central tendency for this dataset?

Solution For this dataset, the mean is

Although this is the center of the data based on the size of the numbers, it is not useful to the retailer since dresses do not come in fractional sizes like 13.25.

The median of the data occurs at the mean of the data in eighth and ninth positions when listed in numerical order. From the frequency table we see that both of the numbers are 14 so the median is 14. This is a dress size, but focusing on reselling only size 14 would not be a good decision. Since size 16 occurs just a frequently among the customers surveyed, we would be overlooking a large portion of her customers if she placed a premium on size 14 only.

It is also possible for every occurrence in a dataset to occur with equal frequency. When this happens, the dataset has no mode.