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More Than Cumulative Frequency

More than cumulative frequency is a statistical measure representing the total number of observations in a dataset that are greater than or equal to the lower limit of a specific class interval. It is calculated by successively subtracting the frequency of each preceding class from the total frequency.

Key Concepts

It is constructed by taking the lower class limits of the grouped data as the reference boundaries.

The first entry in a more than cumulative frequency distribution is always equal to the total frequency (N) of the dataset.

Plotting these cumulative frequencies against their respective lower class limits on a graph produces a downward-sloping curve known as a more than ogive.

Formula & Equation

cf_{k} = N - \sum_{i=1}^{k-1} f_i

cf_k = more than cumulative frequency of the kth class, N = total frequency of the dataset, f_i = simple frequency of the ith preceding class.

Common Misconceptions

Myth: Using the upper limit of the class interval when creating a more than cumulative frequency table.

Fact: For 'more than' cumulative frequency, you must always use the lower limit of the class interval, because you are counting all data points that are greater than or equal to that starting boundary.

Real World Applications

A teacher calculating how many students scored more than 33 marks to quickly find the total number of passing students in a class.

A factory manager determining how many manufactured lightbulbs lasted more than 1000 hours during quality control testing.

Frequently Asked Questions

How do you draw a more than ogive?

Plot the lower class limits on the x-axis and their corresponding more than cumulative frequencies on the y-axis, then join the points with a smooth freehand curve.

How is more than cumulative frequency used to find the median?

By plotting both the less than and more than ogives on the same graph, the x-coordinate of their intersection point gives the exact median of the grouped data.

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