[Notes on a series of lectures given at the Glasgow University, January to March 1913].

  • Brownlee, John, 1868-1927.
Date:
[1913?]
Catalogue details

Licence: In copyright

Credit: [Notes on a series of lectures given at the Glasgow University, January to March 1913]. Source: Wellcome Collection.

Provider: This material has been provided by The University of Glasgow Library. The original may be consulted at The University of Glasgow Library.

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    Constants of Distributions. (1) Mean. If there be a number of quantities of definite measurement, then the ' term mean is used to denote the sum of these measurements divided by the total number of the quantities, or if ... be the measurements, n in number, and M the mean. The term mean as used in .statistics is equivalent to the term arithmetical mean in algebra. (2) Median. 'Phe median is the central value of the group when the measurements are arranged in order of magnitude, so that the number of instances above the median is equal to that below the median. If the groups are at all numerous, it is most easily calculated by simple proportion. Thus, taking the weights of British adults, we find 7749 instances. Of these 3068 are under 1.50 pounds, a defect of 806'5 below the median, and 3122 above 160 pounds, so that the median will be very approximately given by Median = 1504-^^x10 =155-2 lbs. 15o9 The first number is the weight at which the group begins: the multiplier 10 is the value of the group difference, and the fraction the proportional number of the group 1559 to be expected. (3) Mode. This is the mo.st frequent group in asymmetrical distributions, and in symmetrical distributions coincides with the mean and the median. The group in which the mode is situated can usually be easily seen, and if the middle point of this be denoted by zero, the distance of the mode from this can be calculated approximately by the formula m j m. — m, Mode = jT7 L^ r, 2 (m^ — 2m2 4- where n\, m.^, m^ are the numbers included in the successive groups, m^ being that of the group in which the mode is expected. More accurately, the median in general lies between the mode and the mean, so that its distance from the former is twice that from the latter, that is 2(Mean— Median) = Median —Mode, or Mode = 3 x Median — 2 x Mean = 150-8 lbs. in the case previously considered. — 792 By the formula given. Mode = 145 4 ^™ x 10 = 149-2 lbs., Z X or one per cent, of difference.