# 11.1.4 More Means and Medians

## Activity: How Good is Charlie at His Computer Game?

Charlie likes to play a computer game. He plays it every day for six days and records his score. He is happy if he averages more than 450 over the six days. Usually he has high scores, but on Saturday he felt sick and didn’t play very well. Here are his results:

### Charlie’s Scores

Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |

450 | 470 | 430 | 490 | 490 | 220 |

(a) Find Charlie’s mean score over these six days.

### Comment

Remember to order correctly the scores and use the mean if there are an even number of values.

### Answer

(a) To find the mean, find the sum of the scores and divide by the number of scores, six.

So Charlie’s mean score is .

(b) Find Charlie’s median score over these six days.

### Answer

(b) To find the median score, arrange the data values in order:

220 | 430 | 450 | 470 | 490 | 490 |

There is an even number of values (6) so take the mean of the two middle values, 450 and 470.

The mean of 450 and 470 is , so Charlie’s median score is 460.

(c) Would you say that the mean score or the median score is more typical of Charlie’s performance?

### Answer

(c) The low score on Saturday has pulled Charlie’s mean score down, so he might prefer to calculate his average using the median score. It is more typical of the general standard of his scores.

## Activity: Another Computer Game for Charlie

The next week, Charlie starts playing a new computer game. Here are his scores:

### Charlie’s Scores

Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |

250 | 270 | 300 | 290 | 320 | 290 | 270 |

(a) Find Charlie’s mean score over these seven days.

### Answer

(a) To find the mean, find the sum of the scores and divide by the number of scores, seven.

So Charlie’s mean score is (to the nearest whole number).

(b) Find Charlie’s median score over these seven days.

### Answer

(b) To find the median score, arrange the data values in order:

250 | 270 | 270 | 290 | 290 | 300 | 320 |

There is an odd number of values, 7, so Charlie’s median score is the middle value, 290.

(c) How do the median score and the mean score compare this time?

### Answer

(c) This time, the mean score and the median score are quite close. This is because the data values are fairly evenly clustered around the mean value without any extremely high or low values.

11.1.3 Finding the Median of a Data Set