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.