Normal Distribution Curve
‣ Introduction
Contents
‣ Need to understand distribution of data and variability
‣ What is a normal distribution curve ?
‣ Characteristics of Normal Distribution curve
‣ Normal Range
‣ Example of Normal Range
Introduction
‣
Example : Birth weight of Indian children
Descriptive Statistics (summarises the characteristics of a data set )
Mean = 2.5kg
Standard Deviation = 0.3kg
‣ So now the question is what would be normal birth weight of Indian
children ?
We need to understand the distribution of data and
variability
‣
Frequency distribution of data
Birth weight (kgs)
Frequency
1.2 - 1.4
2
1.4 - 1.6
5
1.6 - 1.8
8
1.8 - 2.0
15
2.0 - 2.2
24
2.2 - 2.4
28
2.4 - 2.6
32
2.6 - 2.8
21
2.8 - 3.0
15
3.0 - 3.2
12
3.2 - 3.4
8
3.4 - 3.6
6
What is a normal distribution curve ?
‣ It is a continuous probability distribution for a random variable
‣ It represents the distribution of data in a bell shaped curve in a large sample
‣ It is also known as called Gaussian distribution, after the German mathematician
Carl Gauss who first described it.
Characteristics of a Normal distribution curve
1. The mean, median, and mode are equal. Coincide at the centre point
2. The normal curve is bell-shaped and is symmetric about the mean.
3. The normal curve approaches, but never touches, the x-axis as it extends farther
and farther away from the mean.
4. Standard deviation determines the width of the curve
5. The total area under the normal curve is equal to 1 or 100%. (Means the whole
population is accounted for)
Empirical rule :
▸
Mean ± 1 SD cover 68.27%
▸
Mean ± 2 SD cover 95.45%
▸
Mean ± 3 SD cover 99.73%
These limits on either side of the mean are called "confidence limits" .
Supposing we are considering the 95 % confidence limits .When we say this, it means 95 %
of the area of the normal curve.
Therefore, the probability of a reading falling outside the 95 per cent confidence limits is P <
0.05 or <5%
Normal Range
With certain confidence level or error the normal range is being estimated
With 95% confidence level or 5% error
Normal Range = Mean ± 2 SD
With 99% confidence level or 1% error
Normal Range = Mean ± 3 SD
Example for normal range
‣ From the sample of 100 normal babies the following are observed.
Mean = 2.5 Kgs,
SD
= 0.3 Kgs
1) What is the normal range with 95% confidence level?
2) What is the normal range with 99% confidence level? Or 1% error
Ans. With 95% confidence level or 5% error
Normal range = Mean ± 2 SD
= 2.5 ± 2 (0.3)
= (1.9 to 3.1 ) kgs
With 99% confidence level or 1% error
Normal range = Mean ± 3 SD
= 2.5 ± 3 (0.3)
= (1.6 to 3.4 ) kgs
References
‣
Park's Textbook of Preventive and Social Medicine 26th edition
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