Class frequency
5-29---------------2
30-54--------------------3 3
55-79--------------------4
80—104 5
105-129 2
130-154 1
155-179 1
PC =3(X-Median)/s
median = L +((N/2) – CF)/f *(h)
L=55
(N/2)=9
h=24 f= 4
It is says that median is 77.5, and I could not find it.
I'm not even mention X or s in the Pearson Coefficient or PC,
There is a graph, the points are in the bottom
4.5 29.5
54.5
79.5
104.5
129.5
154.5
179.5
Based on the information provided, it seems like you are trying to find the median of a frequency distribution. The given class frequencies and values indicate the frequency of each class interval.
To find the median, you can use the formula:
median = L + ((N/2) - CF) / f * h
Let's break down the components of the formula:
L: The lower bound of the median class interval (given as 55 in your case)
N/2: The cumulative frequency corresponding to the median position. N is the total number of observations, and in this case, it is not specified. However, the position of the median is given as (N/2) = 9.
CF: The cumulative frequency of the class interval before the median class interval. Based on the given frequencies, the cumulative frequencies increase as follows:
- For class 5-29: 2
- For class 30-54: 2+3=5
- For class 55-79: 5+4=9
So, CF for the class interval before the median interval is 9.
f: The frequency of the median class interval. Based on the given frequencies, the frequency of the median class interval 55-79 is 4.
h: The width of the class intervals (given as 24 in your case).
Now, let's plug in these values into the formula to calculate the median:
median = 55 + ((9/2) - 9) / 4 * 24
median = 55 + (4.5 - 9) / 4 * 24
median = 55 + (-4.5) / 4 * 24
median = 55 - 4.5 / 4 * 24
median = 55 - 1.125 * 24
median = 55 - 27
median = 28
Therefore, based on the given information, the median of the data set is 28.