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Basic Statistics (MEAN)

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Shahirah Aziz
Shahirah Aziz

The mean (or average) of a data set is calculated by summing all the values and dividing by the total number of values. Ungrouped data has not been organized into categories, while grouped data is organized into a frequency distribution table with class intervals, frequencies, and the product of frequency and midpoint. To find the mean of grouped data, the total of the product of frequency and midpoint is divided by the total frequency. The mean, median, and mode are measures of central tendency that analyze where data is centered. The mean is useful when there are no outliers, the median ignores outliers, and the mode finds the most common value.

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Basic Statistics (MEAN)
The mean ( or ) average of a set of data values is the sum of all of the data values divided by the number of data values.
Ungrouped data is a data that has not been organized into groups.
Data that has been organized into groups ( into a frequency distribution) if you see a table similar to the one below, you will know youre dealing with group data.
Example : Find the mean of the grouped data in the given frequency distribution table. Class Interval Frequency (f) Midpoint (x) Product of fx 16-20 2 18 36 11-15 5 13 65 6-10 6 8 48 1-5 9 3 27 Total = 22 176 Table 1.1 Annual Leave Days of 22 State College Employees
The mean, median and mode of a data set are collectively known as measures of central tendency as these three measures focus on where the data is centred or clustered. To analyse data using the mean, median and mode, we need to use the most appropriate measure of central tendency. The following points should be remembered: The mean is useful for predicting future results when there are no extreme values in the data set. However, the impact of extreme values on the mean may be important and should be considered. E.g. The impact of a stock market crash on average investment returns. The median may be more useful than the mean when there are extreme values in the data set as it is not affected by the extreme values. The mode is useful when the most common item, characteristic or value of a data set is required.

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Basic Statistics (MEAN)

  • 2. The mean ( or ) average of a set of data values is the sum of all of the data values divided by the number of data values.
  • 3.
  • 4. Ungrouped data is a data that has not been organized into groups.
  • 5.
  • 6.
  • 7. Data that has been organized into groups ( into a frequency distribution) if you see a table similar to the one below, you will know youre dealing with group data.
  • 8. Example : Find the mean of the grouped data in the given frequency distribution table. Class Interval Frequency (f) Midpoint (x) Product of fx 16-20 2 18 36 11-15 5 13 65 6-10 6 8 48 1-5 9 3 27 Total = 22 176 Table 1.1 Annual Leave Days of 22 State College Employees
  • 9.
  • 10. The mean, median and mode of a data set are collectively known as measures of central tendency as these three measures focus on where the data is centred or clustered. To analyse data using the mean, median and mode, we need to use the most appropriate measure of central tendency. The following points should be remembered: The mean is useful for predicting future results when there are no extreme values in the data set. However, the impact of extreme values on the mean may be important and should be considered. E.g. The impact of a stock market crash on average investment returns. The median may be more useful than the mean when there are extreme values in the data set as it is not affected by the extreme values. The mode is useful when the most common item, characteristic or value of a data set is required.