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Questions and Answers
The arithmetic mean of the following data is _________.
20
The arithmetic mean of the scores 12, 34, 45, 50, 24 is:
If the mean of six observations 5, 7, 9, α, 11 and 12 is 9, then the value of α is:
If the mean of the data 28, 26, 22, 11, 13, x is 20, then find the value of 'x':
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How is the arithmetic mean of grouped data defined?
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Study Notes
Arithmetic Mean
- The arithmetic mean is a way to calculate the average of a set of numbers.
- It is calculated by summing all the observations and dividing by the total number of observations.
- The arithmetic mean is often represented by the symbol "x̄" (pronounced "x-bar").
Mean Formula
- The formula for the arithmetic mean is: x̄ = Σx / n
- Where Σx represents the sum of all the observations, and n represents the number of observations.
Example of Arithmetic Mean
- In the example provided, the cricketer's scores in five ODI matches are: 12, 34, 45, 50, 24.
- To find the average score, we calculate the arithmetic mean: (12 + 34 + 45 + 50 + 24) / 5 = 165 / 5 = 33
Mean of Grouped Data
- When dealing with grouped data, we have frequencies associated with each value.
- Formula for calculating the mean of grouped data: X = Σfixi / Σfi
- Σfixi represents the sum of the product of each value (xi) and its corresponding frequency (fi).
- Σfi represents the sum of all frequencies.
Mean of Discrete Frequency Distribution
- If a variable ‘X’ can take values x1, x2, x3,....., xn with corresponding frequencies f1, f2, f3,....., fn, then the arithmetic mean is:
- X= ( f1x1 + f2x2 + f3x3 +.......+ fnxn) / (f1 + f2 + f3 +.......+ fn)
- This formula is similar to the grouped data mean calculation.
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Description
This quiz covers the concept of arithmetic mean, explaining how to calculate the average of a set of numbers. It includes the formula for the arithmetic mean, examples of calculation, and methods for dealing with grouped data. Perfect for students looking to strengthen their understanding of averages in statistics.
