The class interval arithmetic mean is a measure of central tendency used for grouped data. It provides an estimate of the average value when data is presented in intervals or classes, each with an associated frequency.

The formula for the class interval arithmetic mean is:

\[\bar{x} = \frac{\sum fx}{\sum f}\]

Where:

- \(\bar{x}\) is the arithmetic mean
- \(f\) is the frequency of each class
- \(x\) is the midpoint of each class interval
- \(\sum fx\) is the sum of the products of frequency and midpoint
- \(\sum f\) is the total frequency

- Identify the midpoint of each class interval.
- Multiply each midpoint by its corresponding frequency.
- Sum up all these products (\(\sum fx\)).
- Sum up all the frequencies (\(\sum f\)).
- Divide the sum of products by the total frequency.

Let's calculate the class interval arithmetic mean for the following data:

Class Interval | Frequency (f) | Midpoint (x) | fx |
---|---|---|---|

1-10 | 5 | 5.5 | 27.5 |

11-20 | 20 | 15.5 | 310 |

21-30 | 40 | 25.5 | 1020 |

31-40 | 80 | 35.5 | 2840 |

41-50 | 100 | 45.5 | 4550 |

Total | \(\sum f = 245\) | \(\sum fx = 8747.5\) |

Applying the formula:

\[\bar{x} = \frac{\sum fx}{\sum f} = \frac{8747.5}{245} = 35.70\]

Therefore, the class interval arithmetic mean is 35.70.

This histogram represents the frequency distribution of the class intervals. The red dashed line indicates the calculated arithmetic mean (35.70).

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