Question
Asked Sep 8, 2019

Describe the three measures of central tendency; the mean, median, and mode. Discuss the advantages and disadvantages of each. Explain the impact of outliers on measures of central tendency.

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Expert Answer

Step 1

Measures of central tendency:

These measures are used to identify the central position for the given data. The measures of central tendency includes:

  • Mean
  • Median
  • Mode
Step 2

Mean:

Mean is the measure of central tendency and it is the mathematical average. Mean is calculated by using all data values. Mean is obtained by dividing the sum of all data values by the total number of data values. Moreover, the sum of the deviations taken from the mean is always equal to 0.

Merits of mean:

  • Mean is based on all the observations of the given data.
  • Mean is easy to calculate and simple to understand.
  • Mean is rigidly defined by algebraic formula.

Demerits of mean:

  • Mean is affected by extreme observations.
  • Mean cannot be computed for qualitative data.
  • Mean cannot be computed for the irrelevant data.
Step 3

Median:

The median is the middle value in an ordered sequence of data. If there are no ties, half of the observations will be smaller than the median, and half of the observations will be larger than the median. In addition, the median is unaffected by extreme values in a set of data. Thus, whenever an extreme observation is present, it may be more appropriate to use the median rather than the mean to describe a set of data.

Merits of media...

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