Use the three measures of central tendency (mean, median and mode) in comparing and contrasting sets of ungrouped data. Select and apply a suitable measure given the necessary information
Measures of central tendency are single values that are typical and representative for a group of numbers. They are also called measures of locations. A representative values of location for a group of numbers is neither the biggest nor the smallest but is a number whose values is somewhere in the middle of the group. Such measures are often used to summarize a data set and to compare one data set with another.
Mean
The average value of set of data.
Appropriate for describing measurement data. e.g. heights of people, marks of student papers.
Often influenced by extreme values.
Median
The median of a set of values is defined as the value of the middle item when the values are arranged in ascending or descending order of magnitude.
Mode
The most frequent or repeated value.
In the case of a continuous variable, it is possible that no two values will repeat themselves. In such a situation, the mode is defined as the point of highest Frequency Density, i.e., where occurrences cluster most closely together.
Like the median, the mode has very limited practical use and cannot be subjected to arithmetical manipulation.
However, being the value that occurs most often, it provides a good representation of the data set.
Example 1,
The number of goals in a series of 12 matches are 3, 2, 4, 3, 2, 6, 3, 2, 2, 4, 1, 4.
Find a) the mean b) the mode and c) the median number of goals.
1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 6
a) the mean - 36 / 12 = 3
b) the mode - 2
c) the median - 3 + 3 / 2 = 3
Example 2,
A gardener planted some cucumber seeds in each of 11 pots. The number of seeds that germinated in each pot were 2, 7, 2, 1, 1, 5, 3, 1, 7, 1, 3.
Find a) the mean b) the mode and c) the median
1, 1, 1, 1, 2, 2, 3, 3, 5, 7, 7
a) the mean - 33 / 11 = 3
b) the mode - 1
c) the median - 2 + 2 / 2 = 2
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