Data Management

Lesson

The mean is the **average** of the numbers in a data set.

To calculate the mean, we add up all the scores in a data set, then divide this total by the frequency (ie. number of scores).

Hint

To find the sum of all the scores, we can either add up each individual score, or, if certain scores are repeated, we can add the products of the scores and their frequencies (ie. $f\times x=fx$`f`×`x`=`f``x`). Read through Example 3 to see this in action.

Now let's have a go at calculating the mean of data sets ourselves.

Find the mean of the following scores:

$-14$−14, $0$0, $-2$−2, $-18$−18, $-8$−8, $0$0, $-15$−15, $-1$−1.

Find the mean from the stem-and-leaf plot below:

**Think**: We just need to add up all the scores like before, then divide it by the number of scores.

**Do**:

$\text{Mean }$Mean | $=$= | $\frac{23+28+3\times31+40+43+50+53+2\times58+2\times62+69+71+78+83+2\times90+91}{20}$23+28+3×31+40+43+50+53+2×58+2×62+69+71+78+83+2×90+9120 |

$=$= | $\frac{1142}{20}$114220 | |

$=$= | $57.1$57.1 |

A statistician organised a set of data into the frequency table shown:

Score ($x$x) |
Frequency ($f$f) |
---|---|

$44$44 | $8$8 |

$46$46 | $10$10 |

$48$48 | $6$6 |

$50$50 | $18$18 |

$52$52 | $5$5 |

A) Complete the frequency distribution table:

Score ($x$x) |
Frequency ($f$f) |
$fx$fx |
---|---|---|

$44$44 | $8$8 | $352$352 |

$46$46 | $10$10 | $460$460 |

$48$48 | $6$6 | $288$288 |

$50$50 | $18$18 | $900$900 |

$52$52 | $5$5 | $260$260 |

Totals | $47$47 | $2260$2260 |

B) Calculate the mean correct to $2$2 decimal places.

**Think**: We calculate the mean by dividing the sum of the scores (total $fx$`f``x`) by the number of scores (total $f$`f`)

**Do**:

$\text{Mean }$Mean | $=$= | $\frac{2260}{47}$226047 |

$=$= | $48.0851$48.0851... | |

$=$= | $48.09$48.09 |

The mean of $4$4 scores is $21$21. If three of the scores are $17$17, $3$3 and $8$8, find the $4$4th score (call it $x$`x`).

Calculate the mean for a small set of data and use it to describe the shape of the data set across its range of values, using charts, tables, and graphs (e.g.,“The data values fall mainly into two groups on both sides of the mean.”; “The set of data is not spread out evenly around the mean.”)