## 11 Introduction

In every aspect of our lives, data—information, numbers, words, or images—are collected, recorded, analyzed, interpreted, and used. Us encounter this information in the kind of statistics too—everything from graphs of the latest home sales numbers to census results, the present rate of inflation, or the unemployment rate.

You are watching: Which statement is the most accurate explanation of the information on the graph?

Being able come make sense of data is an important skill. In ar 11.1, us will consider how to summary a set of data by utilizing an median value, calculated making use of the mean, median or mode.

In ar 11.2, we will certainly look at exactly how to present and understand data in tables. The emphasis will then move to graphs, and different varieties of charts the all do data simpler to understand in sections 11.3, 11.4, and 11.5. Graphs and also charts are very useful because that displaying the relationship between quantities quickly and also in an obtainable form, however these can likewise be used to mislead the unwary reader—so you’ll learn just how to critically assess this kind of info too.

Finally, in section 11.6, you"ll see several of the brand-new types of interaction data visualizations that space becoming an ext common.

Check your expertise of averages and also interpreting data native charts and also graphs prior to you start by completing the Unit 11 pre quiz, then use the feedback to aid you setup your study.

The quiz does not check all the object in the unit, but it should give you part idea that the locations you might need come spend many time on. Remember, that doesn’t matter if you acquire some or even every one of the inquiries wrong – it just indicates how much time you may need because that this unit!

Click here for the pre quiz.

### 11.0.1 What to intend in this Unit

This unit have to take roughly ten hrs to complete. In this unit friend will learn about:

The three various averages.Understanding and constructing tables.What to look the end for in charts and graphs.How to construct charts and graphs to display information.## 11.1 Averages

Think the a trip that girlfriend or a friend might take frequently, together asshopping or going come work. How long would certainly you say that trip takes?

You may have actually said miscellaneous like, "Well, it generally takes around 45 minute to acquire to work, but, if the web traffic is heavy, it have the right to take up to hours.” In other words, 45 minute is a typical time, thoughthere room exceptions. Exactly how did you decision what time to say? go you choose a timethat appeared to take place quite often, or probably a time that was somewhere in themiddle the the time taken for current trips?

Knowing a usual value for a data set, and also how the data is spreadout roughly this typical value, is essential for every sorts of situations.

A value that is typical of the worths in a collection of data is well-known as an**average**. There are different ways the calculating an average, and youwill learn about three of these: The **mean**, the **median**, and the**mode**.

### 11.1.1 Calculating the mean of a Data Set

You have probably come throughout the mean before; the is the most typically used form of average and takes into account all the data.

Let’s look at an example to explore this form of average.

Suppose eight students take it an exam, through the adhering to scores:

To obtain a feeling for the problem and to aid you inspect that your final answer is reasonable, look in ~ the test scores and decide what a common value could be. Do a keep in mind of her estimate.

To calculation the typical value, we include all the data values together and then divide this amount by the variety of values.

In this example, the sum of the data values is amount with, 8 , summands ripe plus 7 plus 6 plus 7 plus eight plus four plus 3 plus nine equates to 53.

There space eight data values. Therefore, the median value is 53 divided by eight equals 6.625.

The mean exam score because that these students to be 6.6 (rounded come 1 decimalplace).

How go this compare v the typical value you approximated at the beginning? Did friend decide that 6 or 7 can be a usual value?

The typical value will always lie in between the smallest value and also the biggest value, and will regularly be somewhere in the direction of the middle, though specifically where counts on the actual values in the data set.

Calculating a mean deserve to be summarized as follows:

Add every the values together to find their sum.Count the variety of values.Divide the amount by the variety of values.Write down the conclusion and also include the units.Alternatively, mean value equation left hand side equals right hand side amount of values separated by number of values.

Remember to make a note of this in her math notebook for easy recommendation later.

Take a look at this pencast come see just how to calculation the mean.View document

Activity: detect the typical Time for a Trip

Here’s an example for you to try. The times because that my pilgrimage towork throughout one week last month are presented in the table below:

First, look in ~ the data. What would certainly you to speak is a typicallength of time because that the expedition from this set of data? compose down yourestimate.

Now calculation the typical commute time using the method givenabove.

Answer

The the smallest time is 42 minutes and also the biggest is 58minutes, for this reason a common time would certainly lie in between these, probably 50minutes. Her estimate might be various from this, the course,because it is just a judicious guess at a usual value.

To calculate the mean:

The amount of the worths is sum with, 5 , summands 42 plus 58 to add 45 add to 47 to add 52 amounts to 244.

There are 5 data values, so the average is 244 minutes divided by five amounts to 48.8 minutes.

See more: The Contribution Margin Approach Helps Managers In Short-Term Decision Making Because It ________.

The mean commute time over the week was about 49 minutes.

Remember to incorporate the units. In this case, the systems areminutes.

The median is relatively close come the estimated typical value of 50minutes, so it looks as if the calculated value for the median iscorrect.

### 11.1.2 making use of a Calculator to uncover the Mean

The calculator deserve to be accessed on the left-hand side barunder Toolkit.In the critical activity, you to be asked to calculation the mean of thefollowing commute times:

A student provided the calculator to work out the typical in one step—can girlfriend spot anything the is not correct with exactly how they did this?