Question
Download Solution PDFThe arithmetic mean of the following frequency distribution of number of accidents X on week working days is:
| X: | 2 | 4 | 6 | 8 | 10 | 12 |
| Frequency: | 3 | 4 | 2 | 1 | 4 | 2 |
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is 6.625
Key Points
- Arithmetic mean is a commonly used measure of central tendency that gives an average of a set of numbers.
- The formula for finding the arithmetic mean is: \((sum of data points x frequency) / total frequency.\)
- The arithmetic mean can be sensitive to extreme values in the data set.
- There are other measures of central tendency, such as the median and mode, that can provide a better representation of the data in some cases.
Additional Information
- To find the arithmetic mean (also known as the average), we first need to find the sum of the products of each data point and its frequency, and then divide by the total frequency.
- This can be done as follows:
- \((2 x 3) + (4 x 4) + (6 x 2) + (8 x 1) + (10 x 4) + (12 x 2) = 6 + 16 + 12 + 8 + 40 + 24 = 106\)
- Total frequency = \(3 + 4 + 2 + 1 + 4 + 2 = 16\)
- Arithmetic mean = \(106 / 16 = 6.625\)
- Understanding the concept of central tendency and the various measures used to describe it is important for data analysis and interpretation.
- It is important to choose the appropriate measure of central tendency depending on the type and distribution of the data being analyzed.
Last updated on Jun 13, 2025
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