Chapter 14.4, Problem 1CFU

To determine

To describe:

The median , mean and mode of a set of normal distributed.

Explanation of Solution

Given:

The mean,median and mode of normal distribution.

Concept used:

Normal distribution:- A normal distribution is a frequency distribution that often occurs

There is a large number of values in a set of data.

The graph of this distribution is a symmetric ,bell-shaped curve.

Calculation:

A set of data points is approximately normal if it is mound-shaped and symmetrical.

  $68\%$ of the data fall in with in one standard deviation of the mean.

  $95\%$ of the data fall in with in $2$ standard deviation of the mean.

  $99.97\%$ of the data fall in with in $3$ standard deviation of the mean.

The mean, median and mode might be equal and a distribution may still not be normal

For example :-

  $0,0,0,0,0,0,0,2,2,2,2,3,3,4,5,5,5,5,5,5,5,5,5,6,7,8,8,8,8,10,10,10,10,10,10,10$

The mean , median and mode are each $5$ but the data are not mound-shaped and symmetrical.

This is not normal.