WJEC Maths for AS: Applied sample

2.4 Measures of central tendency (i.e. mean, median and mode) 33 If all the individual values (i.e. x ) in the entire population are known then the population mean can be calculated using the formula μ = ∑  x n where μ is the population mean, ∑  x is the sum of all the individual values and n is the number of values. If the individual values (i.e. x ) in a sample are known the sample mean can be calculated using the formula x = ∑  x n where x is the sample mean, ∑  x is the sum of all the individual values and n is the number of values. The mean of a frequency distribution where the data set is given in a frequency table is calculated using the formula: x = ∑  fx ∑  f   or   μ = ∑  fx ∑  f where x is the sample mean or μ is the population mean, ∑  fx is the sum of all the x values, each multiplied by its frequency, f , and ∑  f is the sum of all the frequencies. Example 1 Find the mean number of peas per pod from the table which shows the number of peas in a pod for a certain type of pea plant. Number of peas in a pod Number of pods 5 3 6 17 7 12 8 10 9 8 10 4 Answer 1 First decide which column of data represents the data values x and which column of data represents the frequency f . As we are interested in the mean number of peas in a pod, the number of peas in a pod is the x -value and the number of pods is the frequency, f. x = ∑  fx ∑  f = (3 × 5) + (17 × 6) + (12 × 7) + (10 × 8) + (8 × 9) + (4 × 10) 3 + 17 + 12 + 10 + 8 + 4 = 393 54 = 7.3 (1 d.p.) This formula will not be given so it must be remembered. If the entire population is used to calculate the mean we give the mean the letter μ . If a sample of the population is used to calculate the mean the mean is given the letter x . Notice both formulas have the same part after the equals. The different letters/ symbols used just tell you whether the data used is the population or a sample. These formulas will not be given, so they need to be remembered. Notice that this is a frequency distribution. There is a single variable (peas in a pod) and the frequency (number of pods).