Statistical Averages and Spreads 0.0 / 5 ? MathematicsStatiscsGCSECCEA Created by: grainne12345Created on: 21-02-19 17:25 Statistical Averages 3 types Mean = Total of all values / Number of values Median = The middle value of an ordered list Mode = Value that occurs most frequently 1 of 17 Statistical Spread Range = Highest value - Lowest value 2 of 17 ---> Comparing The Different Averages 3 of 17 The Mean 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. Advantages Can be calculated exactly Uses all data Disadvantages Influenced by extreme/abnormal values 4 of 17 The Median Advantages Simple to understand Not affected by abnormal values Useful when comparing with a middle value (e.g. half the class got over 50%) Disadvantage Doesn't make use of all the data. 5 of 17 The Mode Advantages 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. Disadvantages Does not make use of all the data. 6 of 17 The Range Useful when we want to investigate the difference between the spread of data. 7 of 17 ---> Finding Averages and the Spread from a Frequency Table 8 of 17 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 9 of 17 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 10 of 17 Mode (Freq. Table) Choose the value with the highest frequency and read across to x. 11 of 17 Range (Freq. Table) The difference between the highest and lowest value of x. 12 of 17 ---> Finding a Missing Value from a Frequency Table when You Have Been Given the Mean 13 of 17 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 14 of 17 ---> Selecting the Most Appropriate Average 15 of 17 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. 16 of 17 Modal class The modal class is the one with the highest frequency. 17 of 17

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