Central Tendency and Variability: Variance and Standard Deviation

Central Tendency and Variability
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Background    The spread of data relates to variations between observed values and a specific data item. The mean and the standard deviation, as well as the variance, are the most frequency used measures of variability/ spread of data.  The range and the interquartile range are also used less frequently, and the measures of spread represent the extent to which data is spread out. The mean is a measure central tendency, and it is typically the starting point when conducting further analysis on data variability. Schofield (2002), highlights on the coefficient of variation which is the standard deviation divided by the mean as a measure that standardizes the measures of dispersion.Variance of the measurements takenlight to Moderate Intensity Physical Activities Deviation SquaredX Mean x-m deviation10 35 -25 625120 35 85 722520 35 -15 22545 35 10 10010 35 -25 62510 35 -25 62510 35 -25 6255 35 -30 90085 35 50 2500 total 13450
Population Variance 13450/9 1494.44Sample variance 13450/ 8 1681.25
Vigorous Intensity Physical Activities
Deviation Squared X Mean x-m deviation 30 49.5 -19.5 380.25 42 49.5 -7.5 56.25 60 49.5 10.5 110.25 65 49.5 15.5 240.25 80 49.5 30.5 930.25 20 49.5 -29.5 870.25 Total 2587.5
Population Variance 2587.5/6 431.25Sample variance 2587.5/5 517.5
Having established the mean to be 35 for the 10 recorded sessions in light to moderate intensity physical activities, calculation of the variance takes into account the addition of the squared deviations from the mean and dividing by the number of observations. As such, the population variance is 13,450/9. However, since the sample size is small the sample variance is 13,450/8. This is also applied to the six observations of vigorous intensity physical activities, where the mean was first calculated and then the deviations. The sample deviation is 2587.5/ 6 while the sample variance is 2587.5/ 5. In the case of vigorous intensity physical activities, there were observations on the sixth day at 65 minutes of running and 60 minutes of yoga. As such, there were two different sessions, and the d...