## Introduction:

In this unit, we will be introducing and discussing data analysis using charts and graphs. Data analysis is an important skill to possess in order to make best judgments based on data trends. In this study guide, we will explore how to decipher information from data illustrations and measurements.

## Chart and Graph Analysis:

Charts, graphs, and tables are crucial forms of measurement and displays of important data. There are many different types of data displays, some of which we will touch on in this unit. The types of data displays that will be discussed in this unit are tables, bar graphs, line graphs, and pie charts.

**Tables**: Data tables are used to organize data in rows and columns to easily process the given information. Consider the following example table of middle school student’s free time throughout the week:

### Student’s Amount of Free-Time (Hours) Throughout The Week

Mon | Tue | Wed | Thu | Fri | Sat | Sun | |

Mary | 4 | 4 | 4 | 4 | 8 | 12 | 3 |

Perry | 5 | 4 | 5 | 4 | 5 | 4 | 4 |

Olly | 3 | 3 | 3 | 3 | 5 | 7 | 7 |

Given a table, interpretations can be made based on the given data. Here is an example: Out of the three students, who has the most free time throughout the week?

To determine which student has the most free time throughout the week, we must add up the hours of free time for each student:

Mary: 4 + 4 + 4 + 4 + 8 + 12 + 3 = 39 hours

Perry: 5 + 4 + 5 + 4 + 5 + 4 + 4 = 31 hours

Olly: 3 + 3 + 3 + 3 + 5 + 7 + 7 = 31 hours

Then it is evident that Mary has the most free time throughout the week.

**Bar Graphs: **Bar graphs are used to visualize data from different categories in order to make comparisons from the information. Consider the following example bar graph of middle school student’s Math test scores between different marking periods:

Given a bar graph, interpretations can be made based on the illustrated data. Here is an example:

What is Mary’s average Math test score for marking periods 1 and 2?

To calculate Mary’s average Math test score, we need to pinpoint both her marking period scores. From the bars next to Mary’s name, we see the first bar goes to 70. This is what Mary scored on the marking period 1 Math test. Similarly, we see the second bar goes to 100. This is what Mary scored on the marking period 2 Math test. Now, we can find the average of these two numbers:

(70 + 100) ÷ 2 = 85

Thus, Mary’s test score average is 85.

**Line Graphs: **Line graphs are used to show trends in data over a period of time. Consider the following example line graph of Mary’s happiness level throughout the school day:

Given a line graph, interpretations can be made based on the data trend. Here is an example: How much does Mary’s happiness level increase from History Class to Lunch?

To determine the increase in Mary’s happiness level from History to Lunch, we need to pinpoint her happiness level at these two points in time. Looking at the line graph we can see that during History Class Mary’s happiness level is 4. If we look along the line graph to Lunch, we can see that Mary’s happiness level is 10. Then to find the amount of happiness increase from History to Lunch, we subtract the History happiness level from the Lunch happiness level:

10 – 4 = 6

So Mary’s happiness increased by 6 from History Class to Lunch.**Pie Chart: **Pie charts are used to show the percentage breakdown of a whole measurement of data. Consider the following example pie chart of the hourly breakdown of Perry’s Saturday activities:

Given a pie chart, interpretations can be made based on the illustrated percentages. Here is an example:

What activity takes up a third of Perry’s Saturday?

In this example, we want to determine which Saturday activity takes up a third of Perry’s day. This means we need to find the activity that takes a third of a full day, or 24 hours. Visually, Sleeping takes up a relatively large portion of Perry’s day so we can start here. Perry sleeps for 8 hours on Saturday. We can check the proportion of hours of sleep to the hours in the day by observing the ratio 8/24. Because 24 is divisible by 8, we can divide the numerator and denominator by 8 which will simplify the ratio to 1/3 . Thus we have confirmed that Sleeping takes up a third of Perry’s Saturday.

## Mean, Median, Mode:

Another way to analyze data is by using the mean, median, and mode of a data set. Mean, median, and mode are measurements used to describe the center of a dataset. Let’s look into each of these measurements more closely.

**Mean: The mean of a data set is the average of numbers in a dataset. **The mean is calculated by adding each value in the dataset and dividing by the total number of values in the dataset.

Example 1

**Find the mean of the following dataset.**

Consider the following dataset of middle school students history test scores in the first marking period:

### Middle School Student’s History Test Scores in Marking Period 1

70, 85, 70, 50, 80, 100, 90, 75, 80, 90

In order to find the mean we will first add all the numbers in the dataset together: 70 + 85 + 70 + 50 + 80 + 100 + 90 + 75 + 80 + 90 = 790

Now we must divide by the number of values in the dataset. Because there are 10 test scores listed in the dataset, we will divide 790 by 10:

790 ÷ 10 = 79.0

Thus, the mean of the dataset is 79.

**Median: The median of a dataset is the middle value of the dataset when the values are arranged from least to greatest. **In the event that there is an even amount of values in the dataset, then the median is the average of the two middle values.

Example 2

**Find the median of the following dataset.**

Consider the following dataset of middle school students history test scores in the first marking period:

### Middle School Student’s History Test Scores in Marking Period 1

70, 85, 70, 50, 80, 100, 90, 75, 80, 90

In order to find the median we will first reorder the test scores from least to greatest:

50, 70, 70, 75, 80, 80, 85, 90, 90, 100

Now we can determine the middle value of the dataset. Because we have an even number of values, we will need to calculate the average of the two middle values:

50, 70, 70, 75, 80, 80, 85, 90, 90, 100

The two middle values of this dataset are 80 and 80. So we will find the average of these two numbers:

80 + 80 = 160

160 ÷ 2 = 80

So, the median of the dataset is 80.

**Mode: The mode of a dataset is the value that appears the most in said dataset. **A data set can have more than one more or none at all.

Example 3

**Find the mode of the following dataset.**

Consider the following dataset of middle school students history test scores in the first marking period:

### Middle School Student’s History Test Scores in Marking Period 1

70, 85, 70, 50, 80, 100, 90, 75, 80, 90

In order to find the mode we will determine how many times each value appears in the dataset:

Dataset Value | Amount of Times Value Appears in Dataset |

50 | 1 |

70 | 2 |

75 | 1 |

80 | 2 |

85 | 1 |

90 | 2 |

100 | 1 |

Because the values that show up the most in the dataset are 70, 80, and 90, all three of these values are the mode of the dataset.