Higher Concepts of Mathematics STATISTICS Frequency Distribution Temperatures Frequency (f) (f)(x_i) 573 574 575 576 578 2 4 5 3 1 15 1146 2296 2875 1728 578 8623 Then calculate the mean, x 1 n n i   1 x_i x 2(573) 4(574) 5(575) 3(576) 1(578) 15 x 8623 15 x 574.9 Variability We have discussed the averages and the means of sets of values.  While the mean is a useful tool in describing a characteristic of a set of numbers, sometimes it is valuable to obtain information about the mean.   There is a second number that indicates how representative the mean is of the data.   For  example,  in  the  group  of  numbers,  100,  5,  20,  2,  the  mean  is  31.75.   If  these  data points represent tank levels for four days, the use of the mean level, 31.75, to make a decision using tank usage could be misleading because none of the data points was close to the mean. Rev. 0 Page 5 MA-05