# Thread: mean, median, mode and range

1. ## mean, median, mode and range

hi, i need to know what the mean, median, mode and range would be for this table. could you explain how you got your answers so i understand!

2. Mode

The x value of 10 has the highest frequency (11). Therefore, the mode is 10.

Mean

To find the mean, a new set of values must be added to the frequency table. This set of values will be called "x * Frequency". In this set of values, the values equal to x multiplied by the frequency. So the values are: 30, 42, 16, 63, 110.

The mean can then be calculated using the formula:
$Mean = \frac{Sum of (x * Frequency)}{Total Frequency}$
$Mean = \frac{261}{31}$
$Mean = 8.4$ (Rounded 1 decimal place)

Therefore the mean is 8.4.

Median

To find the mean, first add up all the frequency values.
$5 + 6 + 2 + 7 + 11 = 31$

Because the number (31) is odd, the median is at the 16th position.
$(\frac{n + 1}{2}) = (\frac{31 + 1}{2}) = 16$

To find out the 16th position, add up the frequencies as follows:

x: 6, 7, 8, 9, 10
F: 5, 6, 2, 7, 11
P: 5, (5 + 6)= 11, (11 + 2) = 13, (13 + 7) = 20, (20 + 11) = 31

The 16th position is after the 13th position and before the 20th position.

Therefore the median is 9.

3. Originally Posted by RogueDemon
Mode

The x value of 10 has the highest frequency (11). Therefore, the mode is 10.

Mean

To find the mean, a new set of values must be added to the frequency table. This set of values will be called "x * Frequency". In this set of values, the values equal to x multiplied by the frequency. So the values are: 30, 42, 16, 63, 110.

The mean can then be calculated using the formula:
$Mean = \frac{Sum of (x * Frequency)}{Total Frequency}$
$Mean = \frac{261}{31}$
$Mean = 8.4$ (Rounded 1 decimal place)

Therefore the mean is 8.4.

Median

To find the mean, first add up all the frequency values.
$5 + 6 + 2 + 7 + 11 = 31$

Because the number (31) is odd, the median is at the 16th position.
$(\frac{n + 1}{2}) = (\frac{31 + 1}{2}) = 16$

To find out the 16th position, add up the frequencies as follows:

x: 6, 7, 8, 9, 10
F: 5, 6, 2, 7, 11
P: 5, (5 + 6)= 11, (11 + 2) = 13, (13 + 7) = 20, (20 + 11) = 31

The 16th position is after the 13th position and the 20th position.

Therefore the median is 7.
thanks very much, do you know how to do the range?

4. Range

The range of x can be calculated as follows:

$r = (greatest value in set) - (lowest value in set)$
$r = 10 - 6$
$r = 4$

Therefore the range of x is 4.

5. Range is MAX - MIN, like already stated.