- Measures of central tendency are statistical methods used in market research to determine the central or typical value of a data set.
- The three common measures of central tendency are mean, median, and mode.
For our calculations we will use the following data which shows sales of a given item by a seller at Gulf Complex each week:
- 10, 12, 13, 14, 14, 15, 16, 17, 18, 20
Mean: Features:
- It is the arithmetic average of all the data values in a set.
- It is sensitive to extreme values or outliers in the data. Calculation:
- Mean = (10 + 12 + 13 + 14 + 14 + 15 + 16 + 17 + 18 + 20) / 10 = 15
Advantages using mean:
- It is easy to calculate and understand.
- It uses all the data values in the calculation, so it is more accurate than other measures. Disadvantages:
- It is affected by outliers, making it less useful in data sets with extreme values.
- It may not be a good representation of the data if the data set is skewed.
Disadvantages of the mean
- It is affected by outliers, making it less useful in data sets with extreme values.
- It may not be a good representation of the data if the data set is skewed.
- It is sensitive to changes in the data set, especially when the data set is small.
- It may not provide a complete picture of the data distribution or variability.
- It can be influenced by missing or incomplete data points, leading to biased results.
- It assumes that the data follows a normal distribution, which may not be true for all data sets.
- It can be misleading if the data set contains extreme values or data points that do not fit the general trend of the data.
Median: Features:
- It is the middle value in a data set when the values are arranged in order.
- It is not affected by outliers in the data set. Calculation:
- Arrange the data set in order: 10, 12, 13, 14, 14, 15, 16, 17, 18, 20
- Median = (14 + 15) / 2 = 14.5
Advantages of using median:
- It is useful in data sets with outliers, as it is not affected by extreme values.
- It is easy to calculate and understand.
Disadvantages of using the median
- It may not use all the data values in the calculation, making it less accurate than the mean.
- It may not be a good representation of the data if the data set is skewed.
- It may not exist or be unique in a data set with an even number of values.
- It does not provide any information on the variability of the data or the distance between data points.
Mode: Features:
- It is the value that occurs most frequently in a data set.
- It is not affected by extreme values or outliers in the data set. Calculation:
- Mode = 14 (since it occurs twice in the data set)
Advantages of using mode:
- It is useful in data sets with outliers or extreme values, as it is not affected by them.
- It is easy to calculate and understand.
Disadvantages of using mode:
- It may not exist or be unique in a data set.
- It may not represent the typical value in a data set if the distribution is not unimodal.
- It is less accurate than the mean or median since it is based only on the most frequent value(s).
