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Topic Content:
- Definition of Arithmetic Mean
- Formula for Calculating Arithmetic Mean
- Worked Example
- Advantages of Arithmetic Mean
- Disadvantages of Arithmetic Mean
What is Arithmetic Mean?
The arithmetic mean is the adding up of all items in a set of data divided by the number of variables. It is the average number in a set of distributions.
Mean is the sum of items or a set of numbers divided by the number of digits.
⇒ \( \scriptsize \bar{x} = \normalsize \frac{\Sigma x}{n} \)
⇒ \( \scriptsize \bar{x} = \normalsize \frac{\Sigma fx}{\Sigma x} \)
Symbols:
x – represents the set of numbers.
n – represents the total number of digits in a set of items.
\( \scriptsize \bar{x}\) – indicates mean or average.
\(\scriptsize {\Sigma} \) – represents the summation of the set of numbers.
f – represents the frequency.
Worked Example 4.2.1:
The scores of five students in Eko Boys Academy who sat for Economics in the May/June 2018 SSCE examination are 35, 35, 34, 40, 46, 40, 45, 45, 30, and 35.
Find the arithmetic mean.
Solution:
⇒ \(\scriptsize \bar{x}= \normalsize \frac{30\:+\:34\:+\:35\:+\:35\:+\:35\\+\:40\:+\:40\:+\:45\:+\:45\:+\:46}{10} \\ \scriptsize \bar{x} = \normalsize \frac{385}{10}\\ \scriptsize \bar{x} = 38.5 \)
Advantages of Arithmetic Mean:
1. Mean is an ideal average and it is stable.
2. Mean is easy to calculate and can be understood without any complications.
3. Mean is very easy to understand.
4. Mean often yields a unique value.
5. Mean is the best central tendency to represent a value in a set of numbers.
6. It is calculated by using all the data in the series.
7. Mean is useful for further statistical work.
8. It makes use of all observations or series given.
9. It enhances efficiency and accuracy.
Disadvantages of Arithmetic Mean:
1. Mean does not reflect true data distribution.
2. Mean may be difficult to calculate if we have large numbers and digits.
3. Mean cannot be obtained graphically.
4. Mean may lead to an unrealistic result if any item of observation is missing.
5. It is impossible to determine without calculation.
6. Arithmetic Mean is not applicable for qualitative data.