The median of the following incomplete frequency distribution is 10:
x= 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8
f= 0 , 2 , 5 , 6, 3 , 1 , 2 , Y
Calculate the frequency of 8
To find the missing frequency (Y) in the frequency distribution, we can use the fact that the median is given as 10.
The median is the middle value of a set of data. In an incomplete frequency distribution, we can determine the median by finding the cumulative frequency that exceeds or is equal to half the sum of all the frequencies.
First, let's find the sum of all the given frequencies (f) in the table:
0 + 2 + 5 + 6 + 3 + 1 + 2 + Y = 19 + Y
Next, we divide this sum by 2 to find half the sum:
(19 + Y) / 2
Now, we need to find the cumulative frequency that exceeds or is equal to this value. We start by adding up the frequencies until we reach this cumulative value.
Given the data:
x = 1, 2, 3, 4, 5, 6, 7, 8
f = 0, 2, 5, 6, 3, 1, 2, Y
The cumulative frequencies are:
0, 2, 7, 13, 16, 17, 19, 19 + Y
Based on the median being 10, we are looking for the cumulative frequency that exceeds or equals (19 + Y) / 2, which is (19 + Y) / 2 = 10.
We can see that the cumulative frequency at x = 4 has reached or exceeded the value 10 (the median). Therefore, the missing frequency (Y) would be the frequency corresponding to x = 8.
From the given data, we can see that the frequency at x = 8 is 2. Therefore, the missing frequency Y is 2.