Describe which measure of central tendency

Describe which measure of central tendency—mean, median, or mode—was probably used in each situation. a. One-half of the factory workers make more than $\$ 5.37$ per hour, and one-half make less than $\$ 5.37$ per hour. b. The average number of children per family in the Plaza Heights Complex is 1.8 . c. Most people prefer red convertibles over any other color. d. The average person cuts the lawn once a week. e. The most common fear today is fear of speaking in public. f. The average age of college professors is 42.3 years.

Describe which measure of central tendency—mean, median, or mode—was probably used in each situation.
a. One-half of the factory workers make more than $\$ 5.37$ per hour, and one-half make less than $\$ 5.37$ per hour.
b. The average number of children per family in the Plaza Heights Complex is 1.8 .
c. Most people prefer red convertibles over any other color.
d. The average person cuts the lawn once a week.
e. The most common fear today is fear of speaking in public.
f. The average age of college professors is 42.3 years.

Key Concepts

Mean

The mean (or average) is calculated by adding all the data points together and then dividing by the number of points. It provides a measure of central tendency that reflects the overall balance point of the data set and is commonly used for numerical data, especially when the distribution is relatively symmetrical without extreme outliers.

Median

The median is the middle value in a data set that has been arranged in order. It divides the data into two equal parts, making it particularly useful for data sets that may be skewed or have outliers, as it is not influenced by extreme values.

Mode

The mode is the most frequently occurring value in a data set. It is the only measure of central tendency that can be used with nominal or categorical data and is helpful in identifying the most common or popular response in a given situation.

Transcript

00:01 The purpose of this exercise is to help you identify the three different central tendencies, mean, median, and mode, and apply them to different situations.

00:11 Let's take a look at part a.

00:12 Part a states that half the workers make more than 537 an hour, and half make less than 537 an hour.

00:19 That use of the more, half less suggests that this is a median.

00:25 Let's put together a sample data set.

00:27 These are all hourly wages.

00:59 Now, if you take a look at these, they're all listed in order, and the number in the middle would be in between 536 and 538, which would be 537 an hour.

01:16 So here's an example of data set that provides this particular answer.

01:21 That makes a a median.

01:41 Let's move on to part b.

01:43 Part b states the average number of children per family is, 1 .8.

01:48 Now, we don't see any one family with 1 .8 children anywhere.

01:54 So, this number is derived by dividing some number of children by some number of families.

02:02 Let's get an example data set here.

02:04 360 children and 200 families would give us 1 .8 children per family.

02:31 So, part of part b is a mean.

02:44 Let's move on to part c.

02:46 Part c states that most people prefer red convertibles.

02:52 Now, color is not something you can put a numeric value on.