# Making Arguments & Predictions from Univariate Data Video

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• 0:42 How To Analyze Univariate Data
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Univariate data is used to describe a situation or experiment; however, you can also use the data to make arguments and predictions. This lesson will show you how to use measures of central tendency to make arguments and predictions.

## Making Predictions from Univariate Data

Sydney has been selling her tomatoes at a local farmer's market for the past year. She sells her tomatoes at \$1 a pound. Her customers are very happy, and they want her to come back again next year. Sydney is now looking at buying a different, more expensive tomato seed. She wants to figure out how many tomato seeds she needs to buy based on last year's sales.

Sydney will need to make a prediction based on the data she has collected. Sydney can use the measures of central tendency to find the number of tomato seeds she needs to purchase. In this lesson, learn how to use the tools of central tendency to make arguments and predictions from univariate data.

## How to Analyze Univariate Data

Univariate data is one variable in a data set that is analyzed to describe a scenario or experiment. Sydney's tomato sales from last year represent a set of univariate data. You may see univariate data in a stem-and-leaf display or in a box-and-whisker plot.

The measures of central tendency are the mathematical concepts that measure the single value that attempts to describe the data set in its entirety. The most common types of measures of central tendency are the mean, median, and the mode. If you are unfamiliar with using these methods, pause this video and check out our other lessons in this statistics course.

These measures or methods are tools we can use to describe a situation. From this description, you can make arguments and predictions from the data. For example, if you were to analyze the heights of each tomato plant and found that the mode of the data is 16 inches, then you could make an argument that the next tomato plant is likely to be 16 inches tall. You can use some or all of the measures of central tendency to analyze your data. It is best to use multiple methods so you can check for mistakes and analyze the data from multiple perspectives.

## Analyzing Data Using Central Tendency

Let's look at Sydney's data from the past year. Each number is the number of tomatoes sold each month for eight months. The data is ordered from least to greatest.

121, 121, 123, 124, 125, 127, 128, 132

Rounded to the nearest whole number, the mean of this data set is 125.

The mean can be used to get an overall idea or picture of the data set. Mean is best used for a data set with numbers that are closer together. Mean is not good for measuring the central tendency of data sets that contain outliers. Since this data set does not contain outliers, we can use the mean of this data set to make arguments and predictions. For example, we could make the argument that Sydney should buy seeds that will yield a minimum of 125 tomatoes, since on average she sold 125 tomatoes each month.

Rounded to the nearest whole number, the median of this set of data is 125. The median can be used to get an idea of what values fall above the midpoint and what values fall below the midpoint. There is equal likelihood that the values in the data set will fall either above or below the median. Median is best used for a data set with numbers that have a few larger or smaller numbers and several numbers close together. One large or small number might skew the mean, but the median can often give you a better idea of the data.

For example, if Sydney sold her tomatoes at the farmers market, and then a sudden storm caused the customers to leave, the sales for that day might skew her data. That's because it wasn't the tomatoes that caused fewer sales, it was the storm. In this case, the median would be a better indicator of central tendency.

The mode is the easiest measure of central tendency to find; simply find the number that occurs the most in the data set. In this data set, the number that occurs the most is 121. Mode is a good way to analyze the frequency that certain numbers occur in a data set. If you are looking for the most popular option in a data set, mode is a good method to use.

Let's look at the measures of central tendency that we have:

Mean: 125
Median: 125
Mode: 121

Based on this data, Sydney would be best off buying at least enough tomato seeds to sell 125 tomatoes each month. We know this because the data set showed us that, on average, Sydney sold 125 tomatoes, while the mode was the smallest number in the data set. We can make the argument that Sydney will need to buy at least enough tomato seeds to sell 125 tomatoes each month. We can also predict that she will sell at least 125 tomatoes on average in the upcoming season.

## Analyzing Data with Graphs and Tables

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