A systematic record of facts or different values of a quantity is called data.
A bar graph is a pictorial representation of data in which rectangular bars of uniform width are drawn with equal spacing between them on one axis, usually the x axis. The value of the variable is shown on the other axis that is the y axis.
A histogram is a set of adjacent rectangles whose areas are proportional to the frequencies of a given continuous frequency distribution
The mean value of a variable is defined as the sum of all the values of the variable divided by the number of values.
The median of a set of data values is the middle value of the data set when it has been arranged in ascending order. That is, from the smallest value to the highest value
Median is calculated as
Where n is the number of values in the data. If the number of values in the data set is even, then the median is the average of the two middle value
Mode of a statistical data is the value of that variable which has the maximum frequency
Mark obtained(x_{i}) |
25 |
35 |
45 |
65 |
No of student(f_{i)} |
4 |
10 |
23 |
34 |
Mean is given by
Class interval |
10-25 |
25-45 |
45-65 |
65-85 |
No of student(f_{i)} |
4 |
10 |
23 |
34 |
In these distribution, it is assumed that frequency of each class interval is centered around its mid point i.e class marks
Where
a=> Assumed mean
d_{i } => x_{i} –a
Where
a=> Assumed mean
u_{i } => (x_{i} –a)/h
Modal class: The class interval having highest frequency is called the modal class and Mode is obtained using the modal class
Where
l = lower limit of the modal class,
h = size of the class interval (assuming all class sizes to be equal),
f_{1} = frequency of the modal class,
f_{0} = frequency of the class preceding the modal class,
f_{2} = frequency of the class succeeding the modal class.
The cumulative frequency of a class is the frequency obtained by adding the frequencies of all the classes preceding the given class.
Class interval ( Age) |
No of Insurance policies |
15-20 |
2 |
20-25 |
4 |
25-30 |
16 |
30-35 |
20 |
35-40 |
20 |
40-45 |
12 |
Cumulative Frequency chart will be like
Age in years |
Cumulative No of Insurance policies |
Less than 20 years |
2 |
Less than 25 years |
6 |
Less than 30 years |
22 |
Less than 35 years |
42 |
Less than 40 years |
62 |
Less than 45 years |
74 |
For the given data, we need to have class interval, frequency distribution and cumulative frequency distribution
Median is calculated as
Where
l = lower limit of median class,
n = number of observations,
cf = cumulative frequency of class preceding the median class,
f = frequency of median class,
h = class size (assuming class size to be equal)
3 Median=Mode +2 Mean