Measures of Central Tendency

Measures of central tendency
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[1] Describe the measures of central tendency. Under what condition each one should be used?
The measures of central tendency describe frequency distributions, they measure location and they include the mean, mode, and median. In choosing the most appropriate measure of central tendency one needs to determine the distribution of data and the type of data.
The mean is the average of the total data, and depends on the sum of all the numbers divided by the number of observations. The metric is appropriate for metric data, but it is also sensitive to the outliers. The mean is preferred to the mode and median as it takes into account numeric data in a frequency distribution (Kvanli, Pavur, & Keeling, 2006).
The mode is the most frequent number in a data set, and depends on the number of times a value is repeated. The mode is used less frequently compared to the mean and median, but is should be used for nominal data, categorical data.
The median is the middle value in a data set, and one needs to arrange the numbers depending on their value beginning with the lowest to highest and then determining the middle value. The median is most appropriate when there is need of ranking data values, and it is associated with ordinal variables (Kvanli, Pavur, & Keeling, 2006). Unlike the mean, the median is not affected by data skewness and outliers.
[2] Last year, 12 employees from a computer company retired. Their ages at retirement are listed below. First, create a stem plot for the data. Next, find the mean retirement age. Round to the nearest year.
55   77   64   77   69   63   62   64   85   64   56   59
Stem plot
Stem
5
569
6
234449
7
77
8
5
Mean=Σx/n= (55+56+59+62+63+64+64+64+69+77+77+85)/12
=795/12=66.25=66 years[3] A retail store manager kept track of the number of car magazines sold each week over a 10-week period. The results are shown below.
27   30   21   62   28   18   23   22   26   28
[a]Mean= Σf /n= (27+30+21+62+28+18+23+22+26+28) = 285/10
=28.5
Median
Data set:18,21,22,23,26,27,28,28,30,62
The median is 26+27/2=26.5
Mode
The dataset:27,30,21,62,28,18,23,22,26,28
The mode=28
[b] The mean is the best measure of central tendency in this case. Even though, it is affected by the outliers, and takes into account all the values in the data set. The highest concentration of values is between 20-30, while there are no values between 40 and 60.
[c] An outlier is an abnormal observation that is inconstant with the other observations, and may be a result of errors, while increasing the sample size reduces the effect of outliers (LeBlanc, 2004). The outlier is I.5 multiplied by the interquartile range, and the values from 13-37 are within normal range, and 62 is the only outlier. A histogram depicting the frequency distribution would also show the range of data, and 62 would ...