Measures of Central Tendency

Application: Measures of Central Tendency

Application: Measures of Central Tendency

The mean of a distribution of values is obtained by adding all of the values and dividing the sum
by the number (Nor n) of values. The mean score is the typical performance level of all the units
sampled. The mean for the burglaries reported in Battawba metropolitan area is given as

APPLICATION: MEASURES OF CENTRAL TENDENCY 2

= 864.1= 864 cases

This means that on average, 864 incidences of burglaries are reported with a standard deviation
of 717 in the Battawba Metropolitan area with the city of Battawba, Wineburg, Drake,Chase
Abbey, Southmetro, Collington Williamson experiencing the highest incidences.
The median represents the middle point of a distribution of data. It is the point at which exactly
half of the observed values in the distribution are higher and half of the observed values are
lower. The Median value for burglaries in Battawba metropolitan area is

MD=689 cases

This implies that 50% of Battawba metropolitan area has a lower than 689 cases of burglary
report and 50% of Battawba metropolitan area has a higher than 689 cases of burglary report
cases (Peavy, Dyal, Eddins, & Centers for Disease Control (U.S.), 1981).
The mode (Mo) is the simplest measure of central tendency and is easy to derive. The
Mode is observed rather than computed. The mode (Mo) of a distribution of values is the value
which occurs most often . The distribution of a given data can either be unimodal if it has only
one mode or bimodal if it has two modes. Other distribution has more than two modes. For the
case of burglaries in Battawba metropolitan area is, the mode is

Mode = 644 cases

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This data has only one mode and its distribution can be said to be unimodal
This value implies that the number of burglary incidences that are frequently reported in
Battawba metropolitan area is 644 cases and most of these are reported in the city of Southmetro
and the city of Williamson. This cities are now our modal cities. These are the cities where most
cases of burglary are frequently reported.
The standard deviation is given as Square root of variance (Grigg, & Transport and Road
Research Laboratory, 1981)

Var (x) = 513689
Sd (x) = 716.721= 717
According to PL,Chebyshev (1821-1894), for any number k greater than 1, atleast (1-1/k 2 ) of the
measurements fall within standard deviation of the mean. That is within the interval (µ-ks, µ+ks)
Where µ is the mean of the sample or population and s is the variance of the sample data or
population. For the case of burglaries in Battawba metropolitan area for k=1, that is one standard
deviation, the interval is (147,1581). This indicates that about 100% of the burglary cases
reported fall within one standard deviation, hence, there is less variations in the burglaries in the

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cities, except for the Battawba city which falls outside the interval. In conclusion, variation
within the data is small. Most of the cases reported are concentrated around the mean.

References

Peavy, J. V., Dyal, W. W., Eddins, D. L., & Centers for Disease Control (U.S.).
(1981).Descriptive statistics: Measures of central tendency and dispersion. Atlanta, Ga:
U.S. Dept. of Health and Human Services/Public Health Service, Centers for Disease
Control.

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Grigg, A. O., & Transport and Road Research Laboratory. (1981). Rating scales: Measures of
central tendency and sample sizes. Crowthorne, Berkshire: Transport and Road Research
Laboratory.
Bridges, J. (1961). Statistics for Selected Secondary–School Students. Education Digest, 27(3),
52-53.