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Data and Prediction
Items of information are called data. Data that is measured often helps us make decisions.

If you are asked how long your journey to school is, the answer would be approximate. You might say "more than 10 minutes" or "usually less than 30 minutes".

To answer the question more precisely, you might make a study of the time for your journey. You would need to write down the times for several days and then work out an average and the range for those journeys.

With these two statistics you give an accurate answer such as "on average it is 14 minutes, and it varies by less than 10 minutes".

Averages
Two averages are often used:

1) Median
The median is the middle value when all the values are placed in increasing order.

e.g. If the journey times are 11 minutes, 13 minutes,
14 minutes, 16 minutes, 21 minutes, the median is 14 minutes.


2) Mean
The mean is the result of adding all the values and dividing the answer by the number of values.

e.g. If the times are 11 minutes, 13 minutes, 14 minutes,
16 minutes, 21 minutes, the mean is:
(11 + 13 + 14 + 16 + 21) ÷ 5 = 75 ÷ 5 = 15 minutes.


The Range
The range of the times is the difference between the longest and shortest journey times.

e.g. If the times are 11 minutes, 13 minutes, 14 minutes,
16 minutes, 21 minutes, the range is 21 - 11 = 10 minutes.


Comparing Data
If journey times need to be compared, both the average and the range give valuable information.

Example
Two students study their journeys to school. They have the same median but different ranges.


Journey to school Student A Student B
Median 13 minutes 13 minutes
Range 5 minutes 10 minutes

Comparing the ranges it would be true to say that "Student B will probably arrive at school after Student A"

When the medians are the same, the range gives additional information.

The mean can be used with the range in the same way as the median.

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