Question

You have a sample of participants and collected data on their monthly income; they reported the exact amount of income that they receive for the entire month rounded to the nearest dollar. You want to report one measure of central tendency that best summarizes the data for this variable. The data are normally distributed. What measure of central tendency should you choose?

Answer 1

Answer:

To measure of central tendency either the mean or median or mode can be used.

Step-by-step explanation:

Measures of Central tendency is a distinct value that describe a data set by recognizing the central location within that data set. The measures of central tendency are every so often are known as measures of central location. They are also known as summary statistics.  

The three measures of central tendency are:

• Mean
• Median
• Mode

The mean is the average value of the data set.

The median is the middle value of the data, when arranged in ascending or descending order.

The mode of the data set is the value with the highest frequency.

The normal distribution is also known as the symmetric distribution.

A normal distribution is an accurate symmetric distribution of experimental data values.  If we create a histogram on data-values that are normally distributed, the figure of columns form a symmetrical bell shape.  The mean, media and mode of the normal distribution coincide.

In this case, the mean, median and mode of the data collected for monthly income are computed. Also it is provided that the data is normally distributed.

As mentioned above, for a normally distributed data:

Mean = Median = Mode

So, any of the three measures of central tendency can be used to best summarizes the data.

Thus, to measure of central tendency either the mean or median or mode can be used.