If there room no too much or outlying worths of a variable, the mean is the most appropriate an overview of a typical value, and to summary variability in the data we particularly estimate the variability in the sample roughly the sample mean.If every one of the observed values in a sample are close to the sample mean, the traditional deviation will be little (i.e., close to zero), and if the observed values vary widely roughly the sample mean, the traditional deviation will certainly be large. If every one of the values in the sample room identical, the sample typical deviation will certainly be zero.

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When discussing the sample mean, we uncovered that the sample typical for diastolic blood push was 71.3. The table listed below showseach that the it was observed values along with its particular deviation indigenous the sample mean. Table 11 - Diastolic Blood Pressures and Deviation indigenous the Sample Mean

X=Diastolic Blood Pressure

Deviation from the Mean

76

4.7

64

-7.3

62

-9.3

81

9.7

70

-1.3

72

0.7

81

9.7

63

-8.3

67

-4.3

77

5.7  The deviations indigenous the mean reflect how much each individual"s diastolic blood pressure is native the average diastolic blood pressure. The an initial participant"s diastolic blood push is 4.7 units over the typical while the 2nd participant"s diastolic blood press is 7.3 units listed below the mean.What we need is a an overview of these deviations native the mean, in details a measure of just how far, top top average, each participant is native the median diastolic blood pressure. If us compute the median of the deviations through summing the deviations and dividing by the sample dimension we run into a problem. The sum of the deviations native the typical is zero. This will constantly be the instance as the is a building of the sample mean, i.e., the sum of the deviations below the mean will always equal the amount of the deviations above the mean.However, the goal is to capture the magnitude of these deviations in a an overview measure. To resolve this difficulty of the deviations summing to zero, we can take absolute values or square every deviation native the mean. Both methods would deal with the problem.

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The an ext popular method to summarize the deviations from the mean requires squaring the deviations (absolute worths are challenging in mathematical proofs).Table 12 below displays every of the observed values, the particular deviations native the sample mean and the squared deviations indigenous the mean.

Table 12

 X=Diastolic Blood Pressure Deviation indigenous the Mean Squared Deviation native the Mean 76 4.7 22.09 64 -7.3 53.29 62 -9.3 86.49 81 9.7 94.09 70 -1.3 1.69 72 0.7 0.49 81 9.7 94.09 63 -8.3 68.89 67 -4.3 18.49 77 5.7 32.49   The squared deviations are interpreted as follows.The first participant"s squared deviation is 22.09 meaning that his/her diastolic blood pressure is 22.09 systems squared from the average diastolic blood pressure, and the 2nd participant"s diastolic blood press is 53.29 devices squared native the average diastolic blood pressure. A quantity that is regularly used to measure up variability in a sample is dubbed the sample variance, and it is essentially the mean of the squared deviations.The sample variance is denoted s2 and also is computed together follows: