Should you use median income or average income statistics to get a more accurate projection of what is occurring in our communities?
Should you use median income or average income statistics? Cubit’s Blog suggests the answer is to use median income data -- either instead of or in addition to – average income data, because outlier data can skew the average. An outlier is a value that "lies outside" most of the other values in a set of data and is much smaller or larger than in value.
It is important to understand the difference between average (mean) income and median income. The average (mean) income is the sum of a set of numbers divided by the count of numbers in the data set. To determine the average, add up all the numbers in the data set and then divide by how many numbers there are in the data set.
Median income is the middle number in the data set, which can be determined by placing all the numbers in value order and finding the middle number in the data set. If there are two middle numbers, then take the average of the two middle numbers to obtain your median income.
So why would you use one over the other? It all comes down to the possibility of an outlier number skewing the result to be less representative of the “average” number.
Statistics for the Terrified discusses using symmetry to determine if the mean or median should be used in data analysis:
The mean is calculated by adding together all the values, and then dividing them by the number of values you have. As long as the data is symmetrically distributed (that is, if when you plot them on a frequency chart you get a nice symmetrical shape) this is fine - but the mean can still be thrown right out by a few extreme values, and if the data is not symmetrical (ie. skewed) it can be downright misleading.
The median, on the other hand, really is the middle value. 50 percent of values are above it, and 50 percent below it. So when the data is not symmetrical, this is the form of “average” that gives a better idea of any general tendency in the data.
So remember: Always use the median when the distribution is skewed. You can use either the mean or the median when the population is symmetrical, because then they will give almost identical results.
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FAQs
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set. Created by Sal Khan.
When should you use mean vs median? ›
The median is a numeric value that separates the higher half of a set from the lower half. When is it applicable? The mean is used for normal number distributions, which have a low amount of outliers. The median is generally used to return the central tendency for skewed number distributions.
Is it better to go by mean or median? ›
Median better when there are outliers. Mean is a parametric estimate (meaning) and is most useful when you know the shape of the distribution. Median is non-parametric (meaning) and there is no need for a distribution shape when used. Mean summarizes using all the data.
What do the mean and median tell us about the data? ›
The median provides a helpful measure of the centre of a dataset. By comparing the median to the mean, you can get an idea of the distribution of a dataset. When the mean and the median are the same, the dataset is more or less evenly distributed from the lowest to highest values.
Why use median income instead of mean? ›
Averages are useful and easy to calculate but can be skewed higher by extremely high outlier incomes at the top end. Medians arrange incomes from lowest to highest, then identify the middlemost income where an equal number fall above and below. This eliminates the outsized influence of outliers.
Why choose median over mean? ›
The median is a better measure of the central tendency of the group as It it is not skewed by exceptionally high or low characteristic values.
How did you decide whether to use the mean or the median? ›
“The mean is typically better when the data follow a symmetric distribution. When the data are skewed, the median is more useful because the mean will be distorted by outliers.”
What is more accurate, mean or median? ›
Mean vs. Median. Accuracy. The median is more resistant to extreme, misleading data values so it would seem to be the clear choice.
When might the median be most useful? ›
The median is the most informative measure of central tendency for skewed distributions or distributions with outliers. For example, the median is often used as a measure of central tendency for income distributions, which are generally highly skewed.
When not to use mean? ›
It is usually inappropriate to use the mean in such situations where your data is skewed. You would normally choose the median or mode, with the median usually preferred.
The mean is the number you get by dividing the sum of a set of values by the number of values in the set. In contrast, the median is the middle number in a set of values when those values are arranged from smallest to largest. The mode of a set of values is the most frequently repeated value in the set.
What does it mean if the mean is higher than the median? ›
The mean is affected by outliers that do not influence the median. Therefore, when the distribution of data is skewed to the left, the mean is often less than the median. When the distribution is skewed to the right, the mean is often greater than the median.
How do you interpret the difference between the mean and median? ›
The mean is the average where the sum of all the numbers is divided by the total number of numbers, whereas the median is the middle value in the list of given numbers numerically ordered from smallest to biggest and mode is the value of the number which occurs most often in the list.
What is a good average salary in the US? ›
With the annual inflation rate for 2023 at 3.4% for the year — up from 3.1% previously — salaries aren't keeping up. A Smart Asset report based on MIT's Living Wage data found that the average salary required to live comfortably in the U.S. is $68,499 after taxes.
When should I use median instead of mean? ›
It's best to use the mean when the distribution of the data values is symmetrical and there are no clear outliers. It's best to use the median when the the distribution of data values is skewed or when there are clear outliers.
What is the disadvantage of using median instead of mean? ›
Disadvantages. It does not take into account the precise value of each observation and hence does not use all information available in the data. Unlike mean, median is not amenable to further mathematical calculation and hence is not used in many statistical tests.
Which is more accurate the mean or median? ›
Mean is generally considered the best measure of central tendency and the most frequently used one.
How do you know if something is the mean or median? ›
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest.
Do you use mean or median for normal distribution? ›
The mean, median, and mode of a normal distribution are equal. The area under the normal curve is equal to 1.0. Normal distributions are denser in the center and less dense in the tails. Normal distributions are defined by two parameters, the mean (μ) and the standard deviation (σ).
Is mean or median better for skewed data? ›
For distributions that have outliers or are skewed, the median is often the preferred measure of central tendency because the median is more resistant to outliers than the mean.
