HISTOGRAM
 A histogram is a graphical representation that
organizes a group of data points into user specified
ranges. Similar in appearance to a bar graph, the
histogram condenses a data series into an easily
interpreted visual by taking many data points and
grouping them into logical ranges or bin.
 Histogram is the data representation in terms of
frequency. It uses binning and is a popular form of data
reduction.
PARTS OF HISTOGRAM
• The Title = The title describes the information
included in the histogram.
• X-axis = The X-axis are intervals that show the scale of
values which the measurement falls under.
• Y-axis = The Y-axis shows the number of times that
the values occur within the intervals set by the X-axis.
FREQUENCY HISTOGRAM
▪︎ A frequency histogram is a histogram that shows the
frequencies ( the number of occurrences ) of the given
data items. For example, in a hospital, there are 20
newborn babies whose ages in increasing order are as
follows: 1,1,1,1, 2,2,2,2,2, 3,3,3,3,3,3,3, 4,4, 5
What Shape is a histogram?
• Histogram is bell shaped of is resembles a bell curve
and has one single peak in the middle of the
distribution.
HISTOGRAM SHAPES
• The histogram can be classified into different types
based on the frequency distribution of the data. There
are different types of distributions, such as normal
distribution, skewed distribution, bimodal distribution,
multimodal distribution, comb distribution, edge peak
distribution, etc. We have mainly 5 types of histogram
shapes.
• Bell Shaped Histogram
• Bimodal Histogram
• Skewed Right Histogram
• Skewed Left Histogram
• Uniform Histogram
BELL SHAPED HISTOGRAM
• A bell shaped histogram has a single peak. The
histogram has just one peak at this time interval and
hence it is a bell shaped histogram. For example, the
following histograms shows the number of children
visiting a park at different time intervals. The histogram
has only one peak. The maximum number of children
who visit the park is between 5:30pm to 6:00pm.
BIMODAL HISTOGRAM
• A bimodal histogram has two peaks. For example, the
following histogram shows the marks obtained by the
48 students of class 8 of St. Mary’s School. The
maximum number of student’s have scored either
between 40 to 50 marks OR between 60 to 70 marks.
SKEWED RIGHT HISTOGRAM
• A skewed right histogram is a histogram that is
skewed to the right. For example, the following
histogram shows the number of people corresponding
to different wage ranges. The histogram is skewed to
the right. For the maximum number of people, wages
ranges from 10-20 ( thousands ).
SKEWED LEFT HISTOGRAM
• A skewed left histogram is a histogram that is skewed
to the left side. For example, the following histogram
shows the number of students of Class 10 of
Greenwood High School according to the amount of
time they spent on their studies on a daily basis. The
maximum number of students study 5.5-5 ( hours ) on
daily basis.
UNIFORM HISTOGRAM
• A uniform histogram is a histogram where all the bars
are more or less of the same height. For example,
Ma’am Lucy, the Principal of Little Lily Play School,
wanted to record the heights of her student. The height
of the students ranges between 30 inches to 50 inches.
RANDOMNESS
• Is a quality or state of being or seeming random ( as in
lacking or seeming to lack a definite plan, purpose, or
pattern ) the metaphor of a coin flip for randomness
remains a questioned.
• An example of a simple random sample would be the
names of 25 employees being chosen out of a hat from
a company of 250 employees.
Individual random events are by definition,
unpredictable but if the probability distribution is
known, the frequency of different outcomes over
different trials is predictable. For example, when
throwing two dice, the outcome of any particular roll is
unpredictable, but the sum of 7 will tend to occur twice
as often as 4.
Run Test of Randomness
• Is a statistical test that is used to know the
randomness in data. Run test of randomness is
sometimes called the Geary tests, and it is non
parametric tests. Run tests of randomness is an
alternative tests to tests autocorrelation in data. Run is
basically a sequence of one symbol such as + or - .
ASSUMPTIONS IN RUN TEST OF RANDOMNESS
1. DATA LEVEL: it is assumed that the data is recorded
in order and not in a group.
2. DATA SCALE: It is assumed that data is in numeric
form.
3. DISTRIBUTION: It is a nonparametric tests.
4. In run tests of randomness, the probability of run is
independent.
UNCERTAINTY
• Is the quantitative estimation of error present
in data; all measurements contain some
uncertainty generated through systematic error
and or random error.
• Any measurement made will have some
uncertainty associated with it, no matter the
precision of the measuring tool.
• For example if you are trying to use a ruler to
measure the diameter of a tennis ball, the
uncertainty might be +-5mm, but if you use Vernier
caliper, the uncertainty could be reduced to maybe
+-2mm.