NORMAL DISTRIBUTION

1. 8
Normal distribution and normal curve
Distribution is the shape and pattern of location of individual
value or data in a set of value or data.
Types of distribution
1. normal distribution [Homogenous distribution]
2. skewed distribution [Heterogeneous distribution]
NORMAL DISTRIBUTION
[Q
1. What do you mean by ‘normal’ distribution? Explain
with examples. (BSMMU, Radiology, January, 2012)
2. Write short notes no: Normal distribution,
(BSMMU, MD Radiology, January 2011, January,
2010, July 2009, January 2009)]
The normal distribution is an extremely important probability
distribution. This distribution is sometimes called the Gaussian
distribution in honor of Carl Friedrich Gauss, a famous
mathematician. The standard normal distribution is the normal
distribution with a mean (μ) of zero and a standard deviation
(σ) of one. Because the graph of its probability density
resembles a bell, it is often called the bell curve.

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Definition
The normal distribution is pattern for the distribution of a set of
data which follows a bell shaped curve.
Or
The normal distribution is a theoretical frequency distribution
for a set of variable data, usually represented by a bell-shaped
curve symmetrical about the mean.
Characteristics normal distribution
[Q: Enumerate the features of normal distribution. BSMMU,
Radiology, January, 2012]
In normal distribution of a large number of observation of any
variable characteristics with small group interval followings are
seen:
1. Some observation are above and others below the mean.
2. If they are arranged in order of magnitude they deviates
towards the extremes from the mean either plus [+] or
minus [-] side and the maximum number of frequency will
be seen around the mean and fewer at the extremes.

3. Biostatistics-63
3. Almost half the observation lie above and half below the
mean and the observation are systematically distributed on
each side of mean.
Arithmetic expression of normal distribution curve
It can be arithmetically expressed as follows in terms of mean
and SD. If they arc known:

4. Biostatistics-64
a. Mean ± 1 SD limits; include 68.27% or roughly 2/3rd of all
the observations. Out of the remaining 1/3rd observations,
half, i.e., 1/6th will lie below the lower limit (mean — 1 SD) and
the other half, i.e., 1 /6th will lie above the upper limit
(mean + 1 SD). In other words. 32% will lie outside the
range, mean ± 1 SD.
b. Mean ± 2 SD limits, Include 95.45% of observations while
4.55% of observations will be outside these limits. Similarly,
mean ± 1.96 SD limits, include 95% of all observations.
c. Mean ± 3 SD limits include 99.73%.
Mean ± 2.58 SI) limits, include 99%.
The normal distribution curve
The normal distribution curve is a symmetrical, bell shaped
graph that has the highest peak in the middle and lowest on the
sides.
Here the frequency distribution is symmetrical around a single
peak so that mean median and mode coincide. It is constructed
from the smallest frequencies at the extremes of classification
to the highest frequency at the peak in the middle.

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Characteristics of a normal curve:
[Q: What are the characteristics of normal curve? (BSMMU,
MD Radiology, July, 2010)]
1. It is bell shaped.
2. Mean, median & mode, coincide
3. It is symmetrical
4. It has two inflections
We can calculate theoretically how many of the observations
will lie in the interval between the mean itself and the mean
plus or minus any multiple of the standard deviation.
Skewed distributions
[Q:
1. What do you mean by skewed' distribution? Explain
with examples. (BSMMU, Radiology, January, 2012)
2. What is normal skewed distribution? (BSMMU, MD
Radiology, January, 2010) ]

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Here sample under study is heterogeneous. They may be
Skewed left or right depending on the long tail of the curve
which may be the left or right of the peak points. Some of them
are also bimodal having two peaks.
Kurtosis
Kurtosis is based on the size of a distribution's tails.
 Distributions with relatively large tails are called "leptokurtic";
Bimodal

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 Those with small tails are called "platykurtic."
 A distribution with the same kurtosis as the normal
distribution is called "mesokurtic."