Five number summary for grouped data calculator

SolutionHelp

1. Calculate the mean and standard deviation for the following distribution

X	6	7	8	9	10	11	12
f	3	6	9	13	8	5	4

2. Calculate the mean and standard deviation for the following distribution

Class	50-55	45-50	40-45	35-40	30-35	35-30	20-25
f	25	30	40	45	80	110	170

Example

1. Calculate Five number summary from the following grouped data
X Frequency
0 1
1 5
2 10
3 6
4 3

Solution:
Five number summary :

Minimum value

=0 $=0$

Maximum value

=4 $=4$

First quartile

Q1 $Q_1$ :

Here,

n=25 $n = 25$

Q1=(n+14)th $Q_1 = ((n+1)/4)^(th)$ value of the observation

=(264)th $=(26/4)^(th)$ value of the observation

=(6.5)th $=(6.5)^(th)$ value of the observation

=2 $=2$

Median

Q2 $Q_2$ :

Q2=(2(n+1)4)th $Q_2 = ((2(n+1))/4)^(th)$ value of the observation

=(2⋅264)th $=((2*26)/4)^(th)$ value of the observation

=(13)th $=(13)^(th)$ value of the observation

=2 $=2$

Third quartile

Q3 $Q_3$ :

Q3=(3(n+1)4)th $Q_3 = ((3(n+1))/4)^(th)$ value of the observation

=(3⋅264)th $=((3*26)/4)^(th)$ value of the observation

=(19.5)th $=(19.5)^(th)$ value of the observation

=3 $=3$

Thus Five number summary is
1. Minimum value

=0 $=0$

2. First quartile

Q1=2 $Q_1=2$

3. Median

Q2=2 $Q_2=2$

4. Third quartile

Q3=3 $Q_3=3$

5. Maximum value

=4 $=4$