# mean, median, mode and range

• Mar 19th 2010, 07:12 AM
andyboy179
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! Attachment 15975
• Mar 19th 2010, 09:00 AM
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:
$\displaystyle Mean = \frac{Sum of (x * Frequency)}{Total Frequency}$
$\displaystyle Mean = \frac{261}{31}$
$\displaystyle Mean = 8.4$ (Rounded 1 decimal place)

Therefore the mean is 8.4.

Median

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

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

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.
• Mar 19th 2010, 09:07 AM
andyboy179
Quote:

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:
$\displaystyle Mean = \frac{Sum of (x * Frequency)}{Total Frequency}$
$\displaystyle Mean = \frac{261}{31}$
$\displaystyle Mean = 8.4$ (Rounded 1 decimal place)

Therefore the mean is 8.4.

Median

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

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

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?
• Mar 19th 2010, 09:16 AM
RogueDemon
Range

The range of x can be calculated as follows:

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

Therefore the range of x is 4.
• Mar 20th 2010, 07:51 AM
funnyname7
Range is MAX - MIN, like already stated.