The document discusses various types of data distributions, highlighting characteristics such as symmetry, peaks, and specific distribution types like normal, binomial, and Poisson. It also covers concepts of skewness and kurtosis, explaining how they describe the shape and peakedness of distributions. Key attributes include definitions of unimodal and bimodal distributions, the bell-shaped normal distribution, and the implications of positive and negative skewness and kurtosis.

2. Graphics displays are useful for
seeing patterns in data. Patterns
in data are commonly described in
terms of center, spread, shape and
unusual features, some common
distribution have special
descriptive labels, such as
symmetry, bell-shaped, skewed.

3. A) Symmetry
B) No. of peaks distribution can have few or many
peaks, distribution with one clear peak are called
UNIMODAL.
* Distribution with two clear peak are called
BIMODAL.
* When a symmetric distribution has a single peak
at the center, it is reffered to as BELL-SHAPED.

4. a) Discrete probability
distribution a
discrete distribution
describes the
probability of
occurrence of each
value of a discrete
random variable.
b) Continuous
probability
distribution a
continuous
distribution describes
the probabilities of
the possible value of
a continuous random
variable.

5.  Three types of distribution
 1) normal 2) binomial 3) poisson
1) NORMAL DISTRIBUTION
if measures
Of distribution are arranged
In linear fashion and vary
Continuously on both the sides from
The central value. The curve
Is also known as “gaussian”
Curve.
* bell shaped.
* symmetrical.

6. It was intoduced by Bernoulli(1680) and is also
known as bernoulli distribution.
 A trial has only two possible outcomes.(success or
failure) ( dead or alive).
 The trial of the experiment are independent of
each other.
 In the trials, the total no. of possible ways of
getting ‘r’ success or failure. (n-r)

7.  Poisson distribution tells about the probability of rare
events.
 Poisson distribution is a
Discrete distribution.
it has a single parameter
Which is the mean of the
Distribution.
for example death due to heart attack in a year.

8. There are two other categories of stastics
which describe the distribution
1) skewness 2) kurtosis
A) skewness distribution can be spread
evenly around both sides of the central
tendency.
* skew review1) negatively skewed distribution-
mean-3,median-5
2) normal distribution- mean-5,median-5
3) positively distribution- mean-7,median-5
a simple way to screen for the direction of the
skew is to substract the median from the mean.

9. 1) If mean-median
results in a positive
no. then the skew is
positive.
2) If mean-median
results in a negative
no. then the skew is
negative.
3) If mean-median
results is zero than
the skew is zero.

10. 1)Kurtosis represents the attributes of flatness.
2) It measures the
Degree of peakedness
Of a frequency distri-
Bution.
3) Kurtosis is a measure
Of the peakedness of the
Probability distribution of
A real valued random variable, it’s the standarized
fourth central moment of a distribution.

11. * kurtosis for the normal distribution is 3.
* positive excess kurtosis indicates flatness ( long, flat tail)
* negative excess kurtosis indicates peakedness.
*kinds of kurtosis
A) Leptokurtic curve leptokurtic curves are those curves
with high peaks and long tail.
or
If the curve is more peaked than a normal curve.
 Where b2 is (beta-two)
 u4 is 4th position
u2 is 2nd position

12. B) Mesokurtic curve Mesokurtic curves are
those curve which have moderately high peak
comparable to the normal. The normal curve
itself is known as mesokurtic curve.
c) Platykurtic curve Platykurtic curve are
those curve which have very flat top for its
peak. These curves are more flat on top than
the normal curve.