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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

The following is a distribution of measurements for a continuous variable. Find the precise median that divides the distribution exactly in half.

Scores: 1, 2, 2, 3, 4, 4, 4, 4, 4, 5

To determine

To find: The median that divides the distribution exactly in half, assuming scores are measurements of a continuous variable.

Explanation

Given info:

The data represents the sample of scores. The scores are: 1, 2, 2, 3, 4, 4, 4, 4, 4, and 5.

Calculations:

Let X denote the continuous scores.

Precise median for a continuous variable:

If there are n observations of a continuous distribution, then the precise median of the distribution is that value, which divides the observations into 2 parts of exactly equal sizes.

Here, number of observations, n=10.

The middle-most part of the given distribution of scores is the (n2)th observation.

n2=102=5

This means that the first 5 observations contain 50% of all observations.

The (n2)th or the 5th observation in ascending order is score X=4.

The scores being continuous, the score X=4 actually corresponds to any value in the interval (3

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