In a continuous frequency distribution, the median of the data is 21.If each observation is increased by 5 find the new median
Answer :
Given :
In a continuous frequency distribution, the median of the data is 21.
And
If each observation is increased by 5 .
Then the new median is also increased by 5 , so new median = 21 + 5 = 26 ( Ans )
We can understand it As :
Suppose there are 20 children and the number of toys with each child is given below :
3, 5, 6, 6, 8, 8, 9, 9, 10, 11, 11, 12, 12, 12, 14, 15, 15, 18, 18, 20
First we form a continuous frequency table , As :
Here frequency is number of children that have toys in between ( 0 -5 , 5 - 10 , 10- 15 , 15 - 20 , 20-25)
Now, median class is 10-15
lower limit of median class = 10
Frequency of median class, f = 7
Cumulative frequency of the class preceeding median class, cf = 8
Class size, h = 5
When each of the given observation is increased by 5, then we get
8,10,11,11,13,13,14,14,15,16,16,17,17,17,19,20,20,23,23,25
Now, median class is 15-20
lower limit of median class = 15
Frequency of median class, f = 7
Cumulative frequency of the class preceeding median class, cf = 8
Class size, h = 5
Given :
In a continuous frequency distribution, the median of the data is 21.
And
If each observation is increased by 5 .
Then the new median is also increased by 5 , so new median = 21 + 5 = 26 ( Ans )
We can understand it As :
Suppose there are 20 children and the number of toys with each child is given below :
3, 5, 6, 6, 8, 8, 9, 9, 10, 11, 11, 12, 12, 12, 14, 15, 15, 18, 18, 20
First we form a continuous frequency table , As :
Number of toys | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20-25 |
Frequency | 1 | 7 | 7 | 4 | 1 |
Here frequency is number of children that have toys in between ( 0 -5 , 5 - 10 , 10- 15 , 15 - 20 , 20-25)
CLASS INTERVALS | Frequency | Cumulative Frequency |
0-5 | 1 | 1 |
5-10 | 7 | 8 |
10-15 | 7 | 15 |
15-20 | 4 | 19 |
20-25 | 1 | 20 |
Now, median class is 10-15
lower limit of median class = 10
Frequency of median class, f = 7
Cumulative frequency of the class preceeding median class, cf = 8
Class size, h = 5
When each of the given observation is increased by 5, then we get
8,10,11,11,13,13,14,14,15,16,16,17,17,17,19,20,20,23,23,25
CLASS INTERVALS | FREQUENCY | CUMULATIVE FREQUENCY |
0-5 | 0 | 0 |
5-10 | 1 | 1 |
10-15 | 7 | 8 |
15-20 | 7 | 15 |
20-25 | 4 | 19 |
25-30 | 1 | 20 |
Now, median class is 15-20
lower limit of median class = 15
Frequency of median class, f = 7
Cumulative frequency of the class preceeding median class, cf = 8
Class size, h = 5