# Data Analysis

## Reading Tables and Drawing Conclusions

Charts and tables are convenient ways to organize data.  The chart below organizes data about students by class and the science class they take.

## Reading Tables and Filling in Missing Data

Charts and tables are convenient ways to organize data.  Usually the trick to reading them is just paying close attention to labels.  A typical grid or table will have labels along one side and the top.  Each cell will contain a value that is unique to the value along the side and along the top.  So, a chart of fees for classes might list classes along the top and dates along the side.

## Scatterplots

Scatterplots are graphs that show how two variables are related. Both the x and y axis of a scatterplot go from low to high values and each pair of data points is plotted on the graph, just like you plot points on a coordinate plane.

Line charts (which are also called line graphs) are graphs that show (using lines that move up and down) how data change over time.  Line graphs are typically used when the x-axis (the horizontal line) is a change in time and the y-axis (vertical) is a change in some other number (amount, price, cost, etc.)

The main goal of a line graph is to show how data change over time, or how the changes in two different sets of data change over time. When you look at a line chart, first look at the title: What is this graph showing me?

Bar charts (which are also called bar graphs and are similar to histograms) are charts that show (using bars of different heights) how data fall into different categories.  Bar charts are used instead of pie charts when the totals do not add up to 100% or when there are many categories.  (Many people like to use line graphs for everything, but line graphs are for things that change over time.  Bar charts are the correct graph to use when you are comparing categories.)

Pie charts are circular charts that are used to show how a whole group is divided into smaller portions.  The entire pie (or circle) represents the whole group or 100%.  Each slice (or section) of the graph represents a particular part of the group, with the pieces sized proportionally.  When you work with pie charts, you often work with percents, so it might be helpful to review the lesson on Percents.

## Range

Range is one of the measures used to describe a dataset.  Range shows what it sounds like -- how far a dataset spans.  Range can be written as a span (e.g., from 10 to 30), but a single measure of range is simple:

Range is the dataset's maximum (highest number) minus its minimum (lowest number).

## Means in Word Problems

Finding a mean or an average in a word problem is often quite simple.

To find a mean, you add up the data points and divide by the number of datapoints.  Because people often find means in real life, it's easy to do word problems of this type.

The simplest type of mean or average word problem simply requires you to read a word problem to find the data, and then find the mean (or average).

## Mean (Average)

Mean is the most commonly used measure of central tendency.  It's often called an average (and sometimes called an arithmetic mean).

To find the mean of a dataset, you add up all of the data points and divide by the number of datapoints.

When dealing with a mean in a word problem, it's often helpful to think of this equation:

$\dfrac{\text{Sum of numbers}}{\text{Number of numbers}}=\text{Mean or Average}$

Let's look at the process of finding a mean in detail:

## Median

Median is a measure of central tendency -- it's a number that can summarize a set of data or a group of numbers.

If you think about driving, the median is the divider in the middle of the road.  Likewise, the median of a set of data is the number in the middle.

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How do you find a median?