# Data

### Chapters

### Calculating Means From Frequency Tables

# Calculating Means From Frequency Tables

Do you remember how to calculate the `mean`

(or the average)? It's the sum of all the scores divided by the total number of scores:

## Example

For example, to find the mean of the scores:

- Find the sum of the scores (add up the scores): \(1 + 17 + 18 + 12 = 48\)
- Divide by the number of scores (\(4\)) to give \(48 \div 4 = 12\)

Sometimes it isn't so simple as being given a list of scores. Our scores (or other data) might be presented in a `frequency table`

like the one below.
The frequency table lists each of the scores, together with its `frequency`

(the number of times it occurs)

Score | Frequency |
---|---|

5 | 6 |

6 | 4 |

7 | 3 |

8 | 2 |

9 | 1 |

10 | 1 |

To find the average of these scores we could do it the hard way, by listing out all the scores, adding them together and dividing by the number of scores like this:

Let's try another example.

### Example

Christo is watching some old British comedies on TV, and laughing his head off. Sam thinks this is hilarious. He decides to work out the average number of times that Christo laughs at an episode. So, he draws up the following frequency table:

Times Christo Laughs in an Episode | Frequency |
---|---|

6 | 10 |

7 | 12 |

8 | 6 |

9 | 4 |

10 | 2 |

Now he needs to work out the mean number of laughing episodes. The answer is

## Summation Notation

We can actually use notation to make our formulas more compact.

The symbol \(\Sigma\) means to add. So, we can write down the sum of our frequencies as \(\Sigma f\), where \(f\) runs over all the frequencies.

In the above example, \(\Sigma f\) would be:

We can also use this notation to add up the products of our scores and their frequencies like this:

Finally, we use the notation \(\overline{x}\) to stand for the mean, so we have the formula:

We can also add columns and rows to our table to keep track of our calculations as follows:

\(x\) | \(f\) | \(fx\) |
---|---|---|

6 | 10 | 60 |

7 | 12 | 84 |

8 | 6 | 48 |

9 | 4 | 36 |

10 | 2 | 20 |

TOTALS |
34 | 248 |

### Description

This chapter series is on Data and is suitable for Year 10 or higher students, topics include

- Accuracy and Precision
- Calculating Means From Frequency Tables
- Correlation
- Cumulative Tables and Graphs
- Discrete and Continuous Data
- Finding the Mean
- Finding the Median
- FindingtheMode
- Formulas for Standard Deviation
- Grouped Frequency Distribution
- Normal Distribution
- Outliers
- Quartiles
- Quincunx
- Quincunx Explained
- Range (Statistics)
- Skewed Data
- Standard Deviation and Variance
- Standard Normal Table
- Univariate and Bivariate Data
- What is Data

### Audience

Year 10 or higher students, some chapters suitable for students in Year 8 or higher

### Learning Objectives

Learn about topics related to "Data"

Author: Subject Coach

Added on: 28th Sep 2018

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