11.1.4 More Means and Medians

Solution symbolActivity: 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.

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Comment

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

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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 equation sequence open sum with, 6 , summands 450 plus 470 plus 430 plus 490 plus 490 plus 220 close divided by six equals 2550 divided by six equals 425.

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

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Answer

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

220 430 450470 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 450 plus 470 divided by two equals 460, 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?

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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.

Solution symbolActivity: 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.

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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 equation sequence open sum with, 7 , summands 250 plus 270 plus 300 plus 290 plus 320 plus 290 plus 270 close divided by seven equals 1990 divided by seven equals 284 postfix (to the nearest whole number).

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

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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?

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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

11.1.5 Finding the Mode of a Data Set