The document discusses skewness in statistical distributions. It defines skewness as asymmetry that causes a curve to appear distorted to the left or right. Negative skewed distributions have a longer left tail, with the mean less than the mode, while positive skewed have a longer right tail and mean greater than the mode. A normal distribution is perfectly symmetrical. Skewness can be measured numerically using Pearson's second coefficient, which involves subtracting the mode from the median and dividing by the standard deviation. An example shows test score data that is negatively skewed, with most values below the mode of 70.

1. WELCOME
ELSA QAZI CAMPUS (FACULTY OF EDUCATION)

2. TOPIC: SKEWNESS
NAME : FARHANA SIDDIQUI
ROLL #: 20
CLASS : B.Ed 2.5 MORNING
ASSIGN BY : Dr. AMJAD ALI ARAIN

3. CONTENT
• DEFINITIONS
• POSITIVE SKEWED
• NEGATIVE SKEWED
• NORMAL CURVE
• MEASURE OF SKEWNESS
• EXAMPLE

4. DEFINITION:
Skewness is asymmetry in a statistical distribution,
in which the curve appears distorted or skewed either
to the left or to the right. Skewness can be quantified to
define the extent to which a distribution differs from a
normal distribution.

5. NEGATIVE SKEWED:
When a distribution is skewed to the left
(red dashed curve), the tail on the curve's
left-hand side is longer than the tail on the
right-hand side, and the mean is less than the
mode. This situation is also called negative
skewness.
POSITIVE SKEWED:
When a distribution is skewed to the right (blue dotted curve), the tail on the
curve's right-hand side is longer than the tail on the left-hand side, and the mean
is greater than the mode. This situation is also called positive skewness.

6. NORMAL CURVE:
In a perfect normal distribution (green solid curve in the illustration below),
the tails on either side of the curve are exact mirror images of each other.
In a normal distribution, the graph appears as a classical, symmetrical "bell-shaped
curve." The mean, or average, and the mode, or maximum point on the curve,
are equal.
MEASURE OF SKEWNESS:
It’s one thing to look at two sets of data and determine that one is symmetric while
the other is asymmetric. It’s another to look at two sets of asymmetric data and say
that one is more skewed than the other. It can be very subjective to determine which
is more skewed by simply looking at the graph of the distribution. This is why there
are ways to numerically calculate the measure of skewness.

7. Pearson’s second coefficient of skewness is also used to measure the asymmetry
of a data set. For this quantity, we subtract the mode from the median, multiply
this number by three and then divide by the standard deviation.
EXAMPLE : A test took place in a class . The
score students obtained from 100 are :
Example of Negative
Skewed::
25
50
56
58
58
58
60
60
60
63
63
68
69
70
70
70
70
75
78 51.5
62.1578
9
-1.84329

8. MEAN =62.157
MEDIAN=51.5
MODE=70
SKEWNESS= -1.8 ( Negative skewed )
The graph and curve represent where the class falls and the
negative skewed represent that class result falls on negative .
25
50
56
58 58 58
60 60 60
63 63
68 69 70 70 70 70
75
78
0
10
20
30
40
50
60
70
80
90
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Chart Title
Series1
MODE