Which measure of central tendency is most appropriate for use with ordinal data

Measure of Central Tendency

We can gain useful information from raw data by organizing them into a frequency distribution and then presenting the data by using various graphs. However, we might be interested in knowing more about our data and describing the data in greater depth. This can be done through  the Measure of Central Tendency ( MCT). 

There are Three types of Measures of Central Tendency:

• Mean:  The average value of the data set 
• Median: The middle value in a data set
• Mode: The most frequent value in a data set

—The Use of MCT depends on the scale of measurement of the data:

Mean

• Mean is the most frequently used MCT. It is the average value in a data set.
• Mean can be calculated for quantitative data ( Interval & Ratio data). 
• ​Mean cannot be calculated for qualitative data ( nominal & ordinal data).
• It is very much susceptible to the presence of extreme values ( high or low values called outliers). In other words, if a data set has an outlier, the value of mean will not be valid. So, data set should be checked for error before performing any analysis. (Cases with values well above or well below the majority of other cases are called outliers)
• The mean is the sum of the values, divided by the total number of values.
• The symbol x̄ (X Bar) represents the sample mean. 
• The symbol μ represents the population mean.
  

• It is also called 50th percentile.
• Median is the middle value in a data set.
• Median is not sensitive to extreme values. The median is affected less than the mean by extremely high or extremely low values.
• It is used to find out whether a data value falls into the upper half or lower half of the distribution. For example,  if we found that the median income for college professors is $40,000, it means that one-half of  the professors earn more than $40,000 and one-half earn less than $40,000.​
• For finding median of a data set, first, we should arrange data in order (Arrange from lowest to highest values).  Second, we should calculate the median location [( n+1)/2] and finally locate the median value. 
• The symbol for the median is MD.                                     
•                                1, 2, 3, 6 ,8, 10,14          MD=6
• When there are an odd number of values in the data set, the median will be an actual data value. 
• When there are an even number of values in the data set, the median will fall between two given values. 

Mode

• Mode corresponds to value with the highest frequency.
• Mode can be calculated for nominal data  such as religious preference, gender, or political affiliation.
• Mode is not sensetive to extreme values ( outliers)
• A data set can be Unimodal, Bimodal, or Multimodal.
• A unimodal data set has only one value with the greatest frequency 
• A bimodal data set has two values  with the same greatest frequency (both values are considered to be the mode )
• A multimodal data set has more than two values  with the same greater frequency (each value is used as the mode)
• ​For example:  6 , 6, 6, 7, 7, 9, 9, 9, 10, 10,10
• When no data value occurs more than once, the data set is said to have no mode. ​

Relationship of the Mean, Median and Mode

--If a frequency distribution has a symmetrical frequency curve, the mean, median, and mode are equal.

• ​If a frequency distribution is positively skewed , then mean is grater than median and median is grater than mode.
• If a frequency distribution is negatively skewed, then mean is less than median and median is less than mode.

Ahmed

11/12/2020 10:32:32

the central locations measures of the ordinal data is the mode NOT mode and median. ISNOT?

Mojgan

11/15/2020 11:29:10

The median is usually preferred to other measures of central tendency when your data set is skewed or you are dealing with ordinal data. However, the mode can also be appropriate in these situations, but is not as commonly used as the median.

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