Question

The frequency distribution below shows the number of children in families at a church in Tucson.

Number of Children	Frequency
0	6
1	12
2	11
3	6
4	3
5	1
6	0

The median number of children in a family is: ______________________

Answer 1

For finding the median of this distribution we need to calculate the cumulative frequencies ( type) of the classes. The cumulative frequency ( type) of any particular class is the sum of all the frequencies up to that class.

Number of children	Frequency	Cumulative frequency ( type)
0	6	6
1	12	6+12=18
2	11	18+11=29
3	6	29+6=35
4	3	35+3=38
5	1	38+1=39
6	0	39+0=39
Total	39

This will let us know where the exact middlemost observation lies. Here total observations/Frequency =39

middlemost value= 39/2=19.5 Hence we need to find the class in which observation number 20 lies. This happens to be 3rd class i.e. Number of children =2 (This is because up to that class there are 29 observations and up to the previous class there are only 18 hence the 20th observation must lie in the second class that is the class with number of children =2

Ans. The median number of children in a family is: 2