Math Tutoring: Averages

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The Study of Averages at eTutorWorld

The mean, median and mode are types of average.

Let’s work out the mode, median and mean of this set of numbers:

7, 9, 11, 5, 13, 5, 5, 3, 11


The mode is the value that appears most frequently.

To work out the mode:

1.Put the numbers in order from smallest to the greatest.
3, 5, 5, 5, 7, 9, 11, 11, 13

2.Look for the number that appears the most.

5 appears more than any other number.

So the mode value is 5.

It is possible to have more than one mode if there is more than one value than which appears the most. A data set can have one mode, more than one mode or no mode at all.


The median is the middle value.

To work out the median:

1.Put the numbers in order from smallest to the greatest.
3, 5, 5, 5,7, 9, 11, 11, 13

2.The number in the middle of the list is the median.
So the median value is 7.

If there are two middle values, the median is halfway between them. Work out the median for this set of numbers:

3, 5, 5, 5, 7, 8, 9, 11, 11, 13

There are two middle values 7 and 8.
The median is halfway between 7 and 8

Add 7 and 8 and divide by 2.


= 7.5

So the median is 7.5.


The mean is the average of the data set .Average is not always a whole number.

To find the mean add all the values and divide by the number of values.

To work out the mean:

1.Add up all the numbers.
7 + 9 + 11 + 5 + 13 + 5 + 5+ 3 + 11 = 69

2.Divide the answer by how many numbers there are.

There are 9 numbers.
69 ÷ 9 = 7.66
So the mean value is 7.66


The range is the difference between the biggest and the smallest number.

To work out the range:

1.Put the numbers in order from smallest to the greatest.
3, 5, 5 ,5,7, 9 ,11, 11 ,13

2.Subtract the smallest number 3 from the biggest number 13.
13 – 3 = 10
so the range of this data set of numbers is 10.

Check Point

  1.  What is the median of the following data set :
    62, 56, 55, 56, 48, 56, 50, 54, 58
  2. Kiara took 7 geography tests in one marking period. What is the range of her test scores?
    88, 73, 84, 92, 87, 75, 94
  3. Find the mean driving speed for 6 different cars on the same highway.
    77 mph,  59 mph,  71 mph,  54 mph, 50 mph, 55 mph
  4. A marathon race was completed by 6 participants. What was the median race time?
    2.7 hr ,9.3 hr,3.6 hr ,5.6 hr ,9.2 hr, 8.1 hr
  5. Find the mode of the following data set :
    55, 47, 38, 63, 56, 64, 44, 63, 39
Answer key
  1. Median= 56
  2. Range = 21
  3. The mean driving speed is 61 mph
  4. The median race time was 6.85 hr
  5. Mode = 63

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