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By James M. Livingstone (auth.)

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The methods which have to be used to achieve accurate results which are still representative 40 THE SCOPE AND METHODS OF MARKET RESEARCH of the population as a whole are fairly sophisticated and beyond the scope of a 'do it yourself' operation. BIASED SAMPLING Finally, and in complete contradiction of all the laws of statistical sampling, there is the case for biased sampling. A situation has already been discussed where there is virtue in biased selection within a sample - that is, going for the person who matters in the decision-making process, particularly in industrial buying.

In group (f) 4 6 II 2 2 n = 25 AN INTRODUCTION TO QUANTITATIVE METHODS 57 This begins to look much simpler. The fact that we chose an assumed mean which coincided with one of the mid-point values cuts out one multiplication. We can now simplify still further. All the class intervals are equal- that is, 4000. , provided of course that we multiply up again by 4000 at a later stage. , times. 8. 8 Mid-point Deviation (d) Frequency (f) fd 4 6 11 2 2 -8 -6(-14) 0 +2 + 4 ( +6) -2 - 1 0 + 1 +2 6 000 10000 14 000 18 000 22 000 n = Arithmetic Mean = assumed Mean 25 fd= -8 + average Deviation = 14 000 + -;~ X 4000 = 14 000 - 1280 12 720 km In statistical language, AM = A + L,jd X class interval n The actual arithmetic mean, calculated from the original data, was 12 636 and the error in this instance was well under 1 per cent.

56, but can easily verify the result by writing down four or five smaller numbers, working out the arithmetic mean and checking that the deviations do cancel out. The nearer the assumed mean is to the actual arithmetic mean, the less tedious the calculations become, but the method works for any assumed mean. (2) This fact gives a clue to the second special case. 56 =12636km 50 THE SCOPE AND METHODS OF MARKET RESEARCH by adding up the actual values and dividing by n is merely a particular case of the 'deviations' method,- that is, the actual values can be thought of as deviations from zero and we are in this sense simply working from an assumed mean of zero.

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