Range, Mode, Median & Mean

Say we have a set of data which contains the values:

1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 7


RANGE:

What would we say the range is?

Well, the range would simply be the highest value, minus the lowest value. So in this case, the range would be:

Highest Value – Lowest Value = 7 -1 = 6

Answer: 6


MODE:

What would we say the mode is?

The mode is the value which appears most often. We know that:

  • 1 appears twice
  • 2 appears twice
  • 3 appears three times
  • 4 appears four times
  • 5 appears two times
  • 6 appears three times
  • 7 appears once

Therefore, in this case – we’d have to call the mode 4.

Answer: 4


MEDIAN:

What would we say the median is?

The median is the value which sits at the centre of all values when they’re lined up in order – from left to right – starting from the lowest value then moving towards the highest value (ascending order). When two different values lie at the centre, you find the mid-point of these two values.

In this case, the median would be:

1, 1, 2, 2, 3, 3, 3, 4, (4), 4, 4, 5, 5, 6, 6, 6, 7

Answer: 4


MEAN:

What would we say the mean is?

The mean in other words – is the average value. You’d find this value by adding up all the values in the set of data,  then dividing this sum by the number of values which exist in the set of data. In the set of data above, there are 17 objects. So, to find the mean of the set of data, we’d have to perform the calculation below:

Mean\\ \\ =\frac { 1+1+2+2+3+3+3+4+4+4+4+5+5+6+6+6+7 }{ 17 } \\ \\ =\frac { 1\times 2+2\times 2+3\times 3+4\times 4+5\times 2+6\times 3+7 }{ 17} \\ \\ =\frac { 66 }{1 7 } \\ \\ 

Answer: 66/17 (Approx: 3.9)


In summary:

Calculation Description Formula
Range Highest value minus the lowest value. None applicable.
Mode Value(s) which appear(s) most often. Most frequent.
Median Middle value when all values are lined up in ascending order. If there are two middle values, you find their mid-point. None applicable.
Mean Sum of all the values (\Sigma x\\ \\ ), divided by the number of values (n\\ \\ ) which exist. \frac { \Sigma x }{ n } \\ \\

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