Combined Arithmetic Mean
The combined arithmetic mean is the arithmetic mean of two or more sets of data. It is calculated by adding up the sums of all the observations in the sets and dividing by the total number of observations.
The formula for the combined arithmetic mean is as follows:
Mean = (∑x₁ + ∑x₂ + ... + ∑xₙ) / (n₁ + n₂ + ... + nₙ)
where:
- Mean is the combined arithmetic mean
- ∑x₁ is the sum of all the observations in the first set
- ∑x₂ is the sum of all the observations in the second set
- …
- ∑xₙ is the sum of all the observations in the nth set
- n₁ is the number of observations in the first set
- n₂ is the number of observations in the second set
- …
- nₙ is the number of observations in the nth set
MCQs on Combined Arithmetic Mean
- What is the combined arithmetic mean?
- The arithmetic mean of two or more sets of data.
- A measure of central tendency that is calculated by adding up the values of all the observations in a set and dividing by the number of observations.
- A measure of variability that is calculated by subtracting the smallest observation from the largest observation in a set.
- A measure of skewness that is calculated by dividing the difference between the mean and the median by the standard deviation.
The correct answer is: The arithmetic mean of two or more sets of data.
- How is the combined arithmetic mean calculated?
- By adding up the sums of all the observations in the sets and dividing by the total number of observations.
- By subtracting the smallest observation from the largest observation in the sets and dividing by the number of observations.
- By dividing the difference between the mean and the median of the sets by the standard deviation of the sets.
- By adding up the means of the sets and dividing by the number of sets.
The correct answer is: By adding up the sums of all the observations in the sets and dividing by the total number of observations.
- What is the effect of increasing the number of sets on the combined arithmetic mean?
- The combined arithmetic mean increases.
- The combined arithmetic mean decreases.
- The combined arithmetic mean does not change.
- The combined arithmetic mean cannot be determined.
The correct answer is: The combined arithmetic mean does not change.
Tips for Using the Combined Arithmetic Mean
- The combined arithmetic mean is a simple and easy-to-calculate measure of central tendency.
- The combined arithmetic mean is not always the best measure of central tendency, especially for skewed distributions.
- The combined arithmetic mean can be used to compare data sets with different sizes.