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More Than Ogive

A more than ogive is a statistical graph that represents the cumulative frequency distribution of grouped data. It is constructed by plotting the lower class boundaries on the x-axis against their corresponding more than cumulative frequencies on the y-axis. This downward-sloping curve is primarily used to visually estimate the median of a dataset.

Key Concepts

To construct it, calculate the more than cumulative frequency by starting with the total frequency and successively subtracting the frequency of each class.

The coordinates plotted on the graph are always in the format (lower class limit, more than cumulative frequency).

The curve always slopes downwards from left to right, unlike the less than ogive which slopes upwards.

The median of the grouped data can be found by locating the point on the x-axis where the more than ogive and less than ogive intersect.

Common Misconceptions

Myth: Students often plot the upper class limits on the x-axis when drawing a more than ogive.

Fact: For a more than ogive, you must always plot the lower class limits on the x-axis. Upper class limits are only used for a less than ogive.

Real World Applications

A school uses a more than ogive to quickly determine how many students scored more than a specific passing mark in a board examination.

A quality control inspector plots a more than ogive to visualize the number of lightbulbs that last more than 500, 1000, and 1500 hours.

Frequently Asked Questions

How do you find the median from a more than ogive?

Calculate \frac{N}{2} (where N is the total frequency), locate this value on the y-axis, draw a horizontal line to the curve, and drop a perpendicular to the x-axis. The x-coordinate is the median.

Why does the more than ogive slope downwards?

It slopes downwards because as the lower class limit increases on the x-axis, the number of observations greater than or equal to that limit naturally decreases.

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