# when would the mode be the most effective way to describe a distribution?

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## FAQs on Measures of Central Tendency

FAQs for the mean, median and mode: measures of central tendency.

## FAQs - Measures of Central Tendency

Please find below some common questions that are asked regarding measures of central tendency, along with their answers. These FAQs are in addition to our article on measures of central tendency found on the previous page.

## What is the best measure of central tendency?

There can often be a "best" measure of central tendency with regards to the data you are analysing, but there is no one "best" measure of central tendency. This is because whether you use the median, mean or mode will depend on the type of data you have (see our Types of Variable guide), such as nominal or continuous data; whether your data has outliers and/or is skewed; and what you are trying to show from your data. Further considerations of when to use each measure of central tendency is found in our guide on the previous page.

## In a strongly skewed distribution, what is the best indicator of central tendency?

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. This is discussed on the previous page under the subtitle, "When not to use the mean".

## Does all data have a median, mode and mean?

Yes and no. All continuous data has a median, mode and mean. However, strictly speaking, ordinal data has a median and mode only, and nominal data has only a mode. However, a consensus has not been reached among statisticians about whether the mean can be used with ordinal data, and you can often see a mean reported for Likert data in research.

## When is the mean the best measure of central tendency?

The mean is usually the best measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data is normally distributed. However, it all depends on what you are trying to show from your data.

## When is the mode the best measure of central tendency?

The mode is the least used of the measures of central tendency and can only be used when dealing with nominal data. For this reason, the mode will be the best measure of central tendency (as it is the only one appropriate to use) when dealing with nominal data. The mean and/or median are usually preferred when dealing with all other types of data, but this does not mean it is never used with these data types.

## When is the median the best measure of central tendency?

The median is usually preferred to other measures of central tendency when your data set is skewed (i.e., forms a skewed distribution) or you are dealing with ordinal data. However, the mode can also be appropriate in these situations, but is not as commonly used as the median.

## What is the most appropriate measure of central tendency when the data has outliers?

The median is usually preferred in these situations because the value of the mean can be distorted by the outliers. However, it will depend on how influential the outliers are. If they do not significantly distort the mean, using the mean as the measure of central tendency will usually be preferred.

## In a normally distributed data set, which is greatest: mode, median or mean?

If the data set is perfectly normal, the mean, median and mean are equal to each other (i.e., the same value).

## For any data set, which measures of central tendency have only one value?

The median and mean can only have one value for a given data set. The mode can have more than one value (see Mode section on previous page).

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## Measures of Central Tendency: Mean, Median, and Mode

In statistics, the three most common measures of central tendency are the mean, median, and mode. Learn how to calculate these measures and determine which one is the best for your data.

## Measures of Central Tendency: Mean, Median, and Mode

By Jim Frost 116 Comments

A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most values in a distribution fall and are also referred to as the central location of a distribution. You can think of it as the tendency of data to cluster around a middle value. In statistics, the three most common measures of central tendency are the mean, median, and mode. Each of these measures calculates the location of the central point using a different method.

Choosing the best measure of central tendency depends on the type of data you have. In this post, I explore these measures of central tendency, show you how to calculate them, and how to determine which one is best for your data.

## Locating the Center of Your Data

Most articles that you’ll read about the mean, median, and mode focus on how you calculate each one. I’m going to take a slightly different approach to start out. My philosophy throughout my blog is to help you intuitively grasp statistics by focusing on concepts. Consequently, I’m going to start by illustrating the central point of several datasets graphically—so you understand the goal. Then, we’ll move on to choosing the best measure of central tendency for your data and the calculations.

The three distributions below represent different data conditions. In each distribution, look for the region where the most common values fall. Even though the shapes and type of data are different, you can find that central location. That’s the area in the distribution where the most common values are located.

As the graphs highlight, you can see where most values tend to occur. That’s the concept. Measures of central tendency represent this idea with a value. Coming up, you’ll learn that as the distribution and kind of data changes, so does the best measure of central tendency. Consequently, you need to know the type of data you have, and graph it, before choosing a measure of central tendency!

**Related posts**: Guide to Data Types and How to Graph Them

The central tendency of a distribution represents one characteristic of a distribution. Another aspect is the variability around that central value. While measures of variability is the topic of a different article (link below), this property describes how far away the data points tend to fall from the center. The graph below shows how distributions with the same central tendency (mean = 100) can actually be quite different. The panel on the left displays a distribution that is tightly clustered around the mean, while the distribution on the right is more spread out. It is crucial to understand that the central tendency summarizes only one aspect of a distribution and that it provides an incomplete picture by itself.

**Related post**: Measures of Variability: Range, Interquartile Range, Variance, and Standard Deviation

## Mean

The mean is the arithmetic average, and it is probably the measure of central tendency that you are most familiar. Calculating the mean is very simple. You just add up all of the values and divide by the number of observations in your dataset.

The calculation of the mean incorporates all values in the data. If you change any value, the mean changes. However, the mean doesn’t always locate the center of the data accurately. Observe the histograms below where I display the mean in the distributions.

In a symmetric distribution, the mean locates the center accurately.

However, in a skewed distribution, the mean can miss the mark. In the histogram above, it is starting to fall outside the central area. This problem occurs because outliers have a substantial impact on the mean. Extreme values in an extended tail pull the mean away from the center. As the distribution becomes more skewed, the mean is drawn further away from the center. Consequently, it’s best to use the mean as a measure of the central tendency when you have a symmetric distribution.

In statistics, we generally use the arithmetic mean, which is the type I discuss in this post. However, there are other types of means, such as the geometric mean. Read my post about the geometric mean to learn when it is a better measure.

**When to use the mean**: Symmetric distribution, Continuous data

**Related posts**: Using Histograms to Understand Your Data and What is the Mean?

## Quiz #2 Flashcards

Start studying Quiz #2. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

## Quiz #2

When would the mode be the most effective way to describe a distribution?

A. When the mean, median, and mode are the same and you have a continuous variable

B. When the mean, median, and mode are the same and you have a categorical variable

C. When data are categorical with few categories

D. The mode is never appropriate

Click card to see definition 👆

C. When the mean, median, and mode are the same and you have a categorical variable

Click again to see term 👆

Kurtosis refers to:

A. whether more extreme scores are in one tail of the distribution as opposed to other

B. the average distance of scores from a measure of central tendency

C. the peakedness or flatness of a distribution

D. whether the distribution is continuous or discrete

Click card to see definition 👆

C. The peakedness or flatness of a distribution

Click again to see term 👆

1/10 Created by ebozadjian

### Terms in this set (10)

When would the mode be the most effective way to describe a distribution?

A. When the mean, median, and mode are the same and you have a continuous variable

B. When the mean, median, and mode are the same and you have a categorical variable

C. When data are categorical with few categories

D. The mode is never appropriate

C. When the mean, median, and mode are the same and you have a categorical variable

Kurtosis refers to:

A. whether more extreme scores are in one tail of the distribution as opposed to other

B. the average distance of scores from a measure of central tendency

C. the peakedness or flatness of a distribution

D. whether the distribution is continuous or discrete

C. The peakedness or flatness of a distribution

Why is the mean the most commonly used measure of central tendency?

A. It isn't the most commonly used

B. The median and the mode don't tell us much when variables are discrete

C. It gives us one, simple number that minimizes deviations overall

D. The mean is more appropriately used to describe variability

C. It gives us one, simple number that minimizes deviations overall

Which of the following values of a distribution's variance is impossible?

A. 1025 B. -.449 C. 2.45 D. .965 B. -.449

Why are measures of variability so important?

A. Because measures of central tendency are so flawed

B. Because standard deviations are not as interpretable as variance

C. Because it tells us how good our measures of central tendency are

D. Because statistics are used only to report variance

C. Because it tells us how good our measure of central tendency are

Why do we transform scores?

A. To get a mean and standard deviation

B. To make different distributions comparable

C. To make life more complicated

D. To change scores to raw units

B. To make different distributions comparable

The Central Limit Theorem tells us that the shape of a sampling distribution of means approaches a normal distribution as:

A. the sample distribution skews positively or negatively.

B. the standard deviation of the population approaches the standard error of the mean.

C. the mean of the population distribution gets larger.

D. the sample size gets larger.

D. The sample size gets larger

The process of selecting a subset of people from a population such that every person in the population has an equal chance of being chosen for the subset is called:

A. standardizing the population

B. stimulus sampling

C. random sampling

D. population sampling

C. Random sampling

A researcher is curious about the average IQ of all currently registered voters in the state of Iowa. If this average could be obtained, it would be an example of a __________.

A. parameter B. statistic C. sample D. population A. Parameter

In addition to telling us at what percentile a given score (or mean) falls, Z scores tell us:

A. our results are likely just due to chance

B. the standardized difference

C. we have proven that our data is different from a population

D. we have disproved that our data is different from a population

B. The standardized difference

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