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Exercise1 (Conversions from Fractions or decimals to Percentages)
Exercise2 (Conversion of percentages to fractions and conversion of percentages to decimal numbers)
Exercise3 (Increasing and Decreasing Percentages)
Exercise4 (Simple Interest)
Exercise 5 (Powers ( Indices ) and Roots)
Exercise6 (Cube Numbers)
Exercise7 - Averages and Range You are here (Exercise 7 - Averages and Range)
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Averages and Range
Introduction
You might be quite familiar with the idea of an "average" from everyday life.
In Mathematics the situation is slightly more complicated, we have three separate ways of expressing an average:
  • the mean
  • the median
  • the mode
Method / Examples
Range
The range is the difference between the highest and lowest figure in a set of data.
For example, for the data:
4, 7, 12, 3, 6, 3, 7, 11, 8, 6
The highest-valued data is 12 and the lowest-valued data is 3, so therefore the range is:
12 - 3 = 9
Mean
To compute the mean (which is normally just called the "average" in everyday life - the average that you most commonly come across), sum all the data items and then divide by the number of data items.
Mean = sum of all the data items / number of data items.
Median
The median is the central value of an ordered distribution.
To obtain the median, order the values from the smallest to the largest. Then pick the middle score. If the data set has an even number of entries, add the two middle values and divide by 2.
or alternatively
The median is that value that has the same number of results above it as below it.
Mode or modal number
The mode is the value that occurs most frequently in the data.
This average can only be computed if the data has some repeated values (and note that there could be more than one mode).
Quiz / Exercises
  1. The weekly wages of ten workers were: £110, £115, £135, £141, £119, £152, £144, £128, £117, £139. Find the mean wage.
  2. The wind speed (in mph) at 8 am on a particular day, was recorded at a number of measuring stations as: 88, 74, 61, 92, 48, 59, 71, 80, 70, 51, 48, 45, 75, 80, 82. Find the mean wind speed.
  3. A rugby team scores 37, 21, 64, 0, 18, 7, 35, 49, 28, 51, 82, 71 points in 12 successive matches. What is its mean score?
  4. The attendances at an art exhibition on six successive days were 130, 97,110, 78, 64 and 150. What was the mean daily attendance?
  5. Seven students scored as follows in a test: 2, 3, 6, 7, 7, 8, 9. The mean score here is 42/7=6. Find the mode.
  1. The number of days spent in hospital by patients on a surgical ward were: 2, 3, 3, 2, 4, 4, 3, 5, 10, 3, 2, 4, 3, 4. Find the mode.
  2. A die was thrown 12 times, and the scores were: 2, 4, 1, 3, 4, 1, 5, 6, 6, 4, 2, 5. What was the median score?
  3. The cost of diesel fuel (per litre) at five garages is 76.8p, 74.2p, 82.9p, 83.7p and 78.9p. What is the median cost?
  4. The ages at which eleven patients were first diagnosed as diabetic were: 5, 12, 16, 18, 25, 16, 17, 57, 32, 60, 61. What was the modal age?
  5. The time taken (in minutes and seconds) to carry out the test on packs of kitchen units was recorded for six quality controllers as: 5:20, 6:40, 5:30, 4:24, 3:58, 4:30. Find the median time taken.
  • Please type your answers (only numerical) into the corresponding spaces below.

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