4.4.2 Averages from Tables and Charts
Mean from discrete data:
To find the mean of discrete data given in a table, use the following formula:
\( mean=\frac{sum\ of (value \times frequency)}{sum \ of \ frequencies} \)
Here are the steps to find the mean of discrete data given in a table:
Identify the discrete values and their corresponding frequencies in the table.
Multiply each value by its corresponding frequency to get the product.
Add up all the products to get the sum of \( (value \times frequency) \).
Add up all the frequencies to get the sum of frequencies.
Plug the sum of \( (value \times frequency) \) and the sum of frequencies into the formula and solve for the mean.
Worked Example:
Suppose we have the following table of discrete data
To find the mean of this data set, we can use the formula:
\( mean= \frac{(2×3)+(4×2)+(6×4)+(8×1)+(10×2)}{3+2+4+1+2} \)
\( mean= \frac{6+8+24+8+20}{12} \)
\( mean= \frac{66}{12} \)
\( mean= 5.5 \)
There fore, the mean of the data set is \( 5.5 \).
Median from discrete data:
To find the median of discrete data presented in a table, use the following steps:
Calculate the total number of observations \( n \).
Determine whether \( n \) is odd or even.
If \( n \) is odd, the median is the value in the middle of the ordered data set.
If \( n \) is even, the median is the average of the two middle values.
Worked Example:
Suppose we have the following table of discrete data:
Calculate the total number of observations \( (n) \)
\( n=20 \)
Determine whether n is odd or even
\( n \) is even
Find the two middle values, which are the \( 10 \)th and \( 11 \)th values
\( 6 \) and \( 8 \)
Take the average of the two middle values to find the median
\( Median= \frac{6+8}{2} \)
\( Median=7 \)
Therefore, the median of the data set is \( 7 \).
Mode from discrete data:
To find the mode of discrete data presented in a table, you need to determine which value or values occur most frequently in the data set.
Here are the steps to find the mode from a frequency table
Look for the highest frequency in the table. This is the frequency of the mode(s).
Identify the corresponding value(s) that have the highest frequency.
If there is only one value with the highest frequency, then that value is the mode.
If there are two or more values with the same highest frequency, then the data set has multiple modes.
Worked Example:
Suppose we have the following table of discrete data
To find the mode of this data set, follow these steps:
Look for the highest frequency in the table.
The highest frequency is \( 4 \), which corresponds to the value \( 6 \).
Identify the corresponding value(s) that have the highest frequency.
The value \( 6 \) is the only value with the highest frequency, so it is the mode.
There fore ,the mode of the data set is \( 6 \).