Normal Probability Curve
This bell shaped curve is called as the ‘Normal
Probability Curve’. Thus the “graph of the probability density function of the
normal distribution is a continuous bell shaped curve, symmetrical about the
mean” is called normal probability curve.
In statistics it is important because:
(а) It is the distribution of many naturally
occurring variables, such as intelligence of 8th grade students, height of the
10th grade students etc.
(b) The distribution of the means of samples drawn
from most parent populations is normal or approximately so when the samples are
sufficiently large.
Therefore normal curve has great significance in
social sciences and behavioral sciences. In behavioral measurement most of the
aspects approximates to the normal distribution. So that Normal Probability
Curve or most popularly known as NPC is used as a reference curve. In order to
understand the utility of the NPC we must have to understand the properties of
the NPC.
Characteristics
of Normal Probability Curve
Some of the major characteristics of normal probability
curve are as follows:
·
The
curve is bilaterally symmetrical. The curve is symmetrical to its ordinate of
the central point of the curve. It means
the size, shape and slope of the curve on one side of the curve is identical to
the other side of the curve. If the
curve is bisected then its right hand side completely matches to the left hand
side.
·
The
curve is asymptotic.
The Normal Probability Curve approaches the horizontal axis and extends
from-∞ to + ∞. Means the extreme ends of
the curve tends to touch the base line but never touch it.
·
The
mean, median and mode. The
mean, Median and mode fall at the middle point and they are numerically equal.
·
The
Points of inflection occur at ± 1 Standard deviation unit. The points of influx in a NPC occur at ± 1σ
to unit above and below the mean. Thus
at this point the curve changes from convex to concave in relation to the horizontal
axis.
·
The
total area of npc is divided in to ± standard deviations. The total of NPC is
divided into six standard deviation units. From the center it is divided in to
three +ve’ standard deviation units and three —ve’ standard deviation units. Thus ± 3σ of NPC include different number of
cases separately. Between ± 1σ lie the middle 2/3rd cases or 68.26%, between ±
2σ lie 95.44% cases and between ± 3σ lie 99.73% cases and beyond + 3σ only
0.37% cases fall.
·
The
y ordinate represents the height of the normal probability curve. The Y ordinate of the
NPC represents the height of the curve. At the center the maximum ordinate
occurs. The height of the curve at the
mean or mid point is denoted as Y0. In
order to determine the height of the curve at any point we use the following
formula:
·
It
is unimodal.
The curve is having only one peak point. Because the maximum frequency
occurs only at one point.
·
The
height of the curve symmetrically declines.
The height of
the curve decline to both the direction symmetrically from the central point.
Means the M + σ and M — σ are equal if the distance from the mean is equal.
·
The
mean of npc is µ and the standard deviation is σ. As the mean of the NPC
represent the population mean so it is represented by the µ (Meu). The standard
deviation of the curve is represented by the Greek Letter, σ.
·
In
normal probability curve the standard deviation is the 50% larger than the
q. In NPC the Q is
generally called the probable error or PE.
The relationship between PE and a can be
stated as following:
1 PE = .6745σ
1σ = 1.4826PE
- The
average deviation about the mean of npc is .798σ. There is a
constant relationship between standard deviation and average deviation in
a NPC.
- The
model ordinate varies increasingly to the standard deviation. In a Normal Probability curve the modal
ordinate varies increasingly to the standard deviation. The standard deviation of the Normal
Probability Curve increases, the modal ordinate decreases and vice-versa.
FIGURE1.
Normal Probability Curve
TABLE 1. Merits and Demerits of
Npc
MEERITS
|
DEMERITS
|
Accurate For Large Class
|
|
Above 200 Students
|
Less than 200 Students
|
Healthy
|
Unhealthy
|
VIDEO PRESENTATION USING DU RECORDER
MY AUDIO
POWER POINT PRESENTATION OF NPC
