If there are no excessive or outlying worths of a variable, the median is the most appropriate review of a common value, and to summarize variability in the data we specifically estimate the variability in the sample about the sample mean.If all of the observed values in a sample are close to the sample mean, the standard deviation will certainly be small (i.e., close to zero), and also if the observed values vary widely around the sample mean, the traditional deviation will be large. If every one of the worths in the sample room identical, the sample standard deviation will certainly be zero.

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When pointing out the sample mean, we uncovered that the sample mean for diastolic blood press was 71.3. The table below showseach of the observed values along with its respective deviation native the sample mean.

Table 11 - Diastolic Blood Pressures and Deviation native the Sample Mean

X=Diastolic Blood Pressure

Deviation indigenous 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 far each individual"s diastolic blood pressure is indigenous the median 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 push is 7.3 units below the mean.What we need is a summary of this deviations native the mean, in particular a measure of exactly how far, ~ above average, each participant is indigenous the average diastolic blood pressure. If us compute the median of the deviations through summing the deviations and dividing by the sample dimension we run right into a problem. The sum of the deviations from the average is zero. This will always be the instance as it is a building of the sample mean, i.e., the sum of the deviations listed below the average will always equal the sum of the deviations above the mean.However, the score is to record the magnitude of these deviations in a an introduction measure. To attend to this difficulty of the deviations summing to zero, we could take absolute worths or square each deviation indigenous the mean. Both techniques would resolve the problem.

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The an ext popular technique to summary the deviations from the mean involves squaring the deviations (absolute worths are complicated in math proofs).Table 12 listed below displays each of the observed values, the particular deviations from the sample mean and also the squared deviations from the mean.

Table 12

 X=Diastolic Blood Pressure Deviation indigenous the Mean Squared Deviation from 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 an initial participant"s squared deviation is 22.09 meaning that his/her diastolic blood push is 22.09 devices squared indigenous the mean diastolic blood pressure, and the 2nd participant"s diastolic blood pressure is 53.29 systems squared indigenous the average diastolic blood pressure. A amount that is frequently used to measure up variability in a sample is referred to as the sample variance, and it is essentially the mean of the squared deviations.The sample variance is denoted s2 and is computed together follows: