Question

Why in normal distribution, 1 standard deviation of the mean is 68% and 2 standard deviations of the mean is 95%? How can we calculate it?

Answer 1

Take haep from this and flourish u r answer
Data can be "distributed" (spread out) in different ways.

It can be spread out more on the left ... or more on the right

Or it can be all jumbled up



But there are many cases where the data tends to be around a central value with no bias left or right, and it gets close to a "Normal Distribution" like this:



A Normal Distribution

The "Bell Curve" is a Normal Distribution.
And the yellow histogram shows some data that follows it closely, but not perfectly (which is usual).

It is often called a "Bell Curve"
because it looks like a bell.
Many things closely follow a Normal Distribution:

heights of people
size of things produced by machines
errors in measurements
blood pressure
marks on a test
We say the data is "normally distributed".

The Normal Distribution has:

mean = median = mode
symmetry about the center
50% of values less than the mean
and 50% greater than the mean

Quincunx
You can see a normal distribution being created by random chance!

It is called the Quincunx and it is an amazing machine.

Have a play with it!


Standard Deviations
The Standard Deviation is a measure of how spread out numbers are (read that page for details on how to calculate it).

When you calculate the standard deviation of your data, you will find that:




68% of values are within
1 standard deviation of the mean









95% are within 2 standard deviations









99.7% are within 3 standard deviations



Example: 95% of students at school are between 1.1m and 1.7m tall.
Assuming this data is normally distributed can you calculate the mean and standard deviation?
The mean is halfway between 1.1m and 1.7m:
Mean = (1.1m + 1.7m) / 2 = 1.4m
95% is 2 standard deviations either side of the mean (a total of 4 standard deviations) so:
1 standard deviation = (1.7m-1.1m) / 4
= 0.6m / 4 = 0.15m

hope it helps! :)

Answer 2

thanks for replying :) it does help me to understand 'normal distribution' more, however it doesn't explain why is it 68% within 1 standard deviation of the mean.. thanks anyway :)

Answer 3

i would n't!!