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# Statistical Questions

Statistics is one branch of applied mathematics that involves collecting meaningful data and information, analyzing it, and using it to make informed decisions. Statistics is used in virtually every field of study and industry there is. We constantly hear about employment statistics, financial statistics, educational statistics, and more. Businesses use statistics to make decisions about where to expand and where to contract their business models. Schools use statistics to designate resources where they will have the most effect, as do governments and other entities.

Statistics begin with questions, which we'll discuss below.

## What is a statistical question?

A statistical question doesn't look for just one answer. Instead, statistical questions generate a wide variety of different answers. The statistician is interested in the distribution and tendency of those answers.

As an example, "How old are you?" is not a statistical question. On the other hand, "What is the median age of the members of your department?" is a statistical question.

## Central tendency

If the answers to the statistical question are numbers, or numerical data, we can look at the central tendency of the information. For example, if we asked how old the members of your department are, we might want to ask how old most people in your department are.

It's important to note that this is not a precise question. We can measure the central tendency using a single number by finding the mean, median, or mode of the information.

Another word for the mean is the average of the data. This is the sum of all the data divided by the total number of data points. So if you had 100 people in your department and their ages added up to 4100, the mean age of people in your department would be 41.

The median is the central data point in a set of numbers once arranged from smallest to largest (or largest to smallest). If you have an odd number of data points, this is the middle number. If you have an even number of data points, it is the average between the two center data points. While the average age of your coworkers might be 41, the median could be a different number, such as 38 or 46, or whatever age lies right in the middle of the other ages. The advantage of the median is that it is less influenced by outliers in the data set.

The mode is the number in a set of numbers that occurs the most frequently. This could be misleading because you could have an average (mean) age of 41 and a median age of 46, but if you have five people who are 26 and only one or two people of every other age, your mode is 26, which makes it sound like most people in your department are 26. That's why central tendency is an imprecise question with imprecise answers. However, if you find the mean, median, and mode, you generally get a good idea of the central tendency.

## Variation

Knowing that the average age of people in your department is 41 is interesting, but it doesn't give a full picture. You may still be interested in the entire spread of data. Is everybody near 41, within 5 years, or are there a lot of much younger and much older people?

The easiest way to measure the variation of data is the range, which is calculated by subtracting the lowest value from the highest value. There are also more complex measures of variation, including the interquartile range and the standard deviation or variance.

Here is a graph of two data sets. They show the number of students in two different schools who got a particular score on a 10-point quiz.

Both data sets have the same range, which is 10, and the same mean, which is a little more than 6. Both also have about the same number of students, which isn't easy to tell from the graph, but it is true. However, the variance is much greater with the blue bars than with the orange bars. This shows how you need to use a variety of statistical models to get a complete picture of statistical information.

Mode

Variance

## Flashcards covering the Statistical Questions

Statistics Flashcards

## Get help learning about multiplying and dividing with negatives

If your student is struggling to understand the difference between a statistical question and a regular question, they may need help from a tutor. A statistical tutor can help your student with this and other aspects of statistics and probability. Tutors can work at your student's pace, making their tutoring time efficient and effective. Contact Varsity Tutors today to speak to one of our Educational Directors and learn how tutoring can help your student's understanding of statistical questions.

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