- Created by: grainne12345
- Created on: 21-02-19 17:25
Mean = Total of all values / Number of values
Median = The middle value of an ordered list
Mode = Value that occurs most frequently
Range = Highest value - Lowest value
Comparing The Different Averages
Gives an idea of what would happen if there were equal shares.
Useful when you need to quote a typical value provided that the data is quite closely grouped around the mean.
- Can be calculated exactly
- Uses all data
- Influenced by extreme/abnormal values
- Simple to understand
- Not affected by abnormal values
- Useful when comparing with a middle value (e.g. half the class got over 50%)
- Doesn't make use of all the data.
- Simple to understand.
- Not affected by abnormal values.
- Useful to manufacturers and shops of shoes and clothes. (e.g. which shoe size is most popular)
- Useful in opinion polls and appropriate for non-numeric data.
- Does not make use of all the data.
Useful when we want to investigate the difference between the spread of data.
Finding Averages and the Spread from a Frequency Table
Mean (Freq. Table)
- Multiply each value (x) by its frequency (f) to get fx.
- Add up the fx values to get Σfx (Σ = Total)
- Add up all the f values to get Σf
Mean = Σfx / Σf
Median (Freq. Table)
- Add up all the frequencies to get the total frequency. Σf
- Divide this total by 2. This gives us the position of the median.
- On your table, construct a cumulative frequency column. (The last value should be the same as the Σf)
- (Cum. Freq. = add the second frequency to the first, then add the third to that total, then the forth to that total and so on)
- Find the value corresponding to the position of the median by reading across to x.
Median's position = Σf / 2
Mode (Freq. Table)
Choose the value with the highest frequency and read across to x.
Range (Freq. Table)
The difference between the highest and lowest value of x.
Finding a Missing Value from a Frequency Table when You Have Been Given the Mean
Finding n from a Freq. Table
- Create an fx column (and an x column if you are working with a grouped freq. table.)
- Total all the columns.
- Fill out the Σfx / Σf
- Beside that put your mean / 1
- Cross multiply
- Finish equation
- Your answer should always be positive and a whole number
Selecting the Most Appropriate Average
The Most Appropriate Average
Mean = When all the values must be taken into account.
Median = When there are one or two abnormal values.
Mode = When you want the most popular value.
Mode = When the values are not numerical.
The modal class is the one with the highest frequency.