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 calculate the frequency of 8 in the given incomplete frequency distribution, we need to use the information given.
We are told that the median of the distribution is 10. The median is the middle value of a dataset when it is arranged in ascending or descending order. In this case, we can see that the values in the 'x' column are already in ascending order.
Now, let's calculate the cumulative frequency (CF) by adding up the values in the 'f' column:
CF = 0 + 2 + 5 + 6 + 3 + 1 + 2 + Y
The median is the value that has a cumulative frequency (CF) equal to or greater than half of the total frequency (N/2). In this case, the total frequency N is the sum of all the values in the 'f' column.
Since the median is given as 10, we know that the total frequency N must be greater than or equal to 20 because the median is the middle value. Therefore, the sum of the frequencies must be at least 20.
Let's do some calculations:
N = 0 + 2 + 5 + 6 + 3 + 1 + 2 + Y
Since Y is unknown, we can solve for it using the condition that the sum of the frequencies should be at least 20:
0 + 2 + 5 + 6 + 3 + 1 + 2 + Y ≥ 20
19 + Y ≥ 20
Subtracting 19 from both sides:
Y ≥ 20 - 19
Y ≥ 1
Therefore, the frequency of 8 must be at least 1 to make the total frequency at least 20.