How to find cf in median class 11?
Table of Contents:
As discussed above, the median is one of the measures of central tendency, which gives the middle value of the given data set. While finding the median of the ungrouped data, first arrange the given data in ascending order, and then find the median value.
If the total number of observations (n) is odd, then the median is (n+1)/2 th observation.
If the total number of observations (n) is even, then the median will be average of n/2th and the (n/2)+1 th observation.
For example, 6, 4, 7, 3 and 2 is the given data set.
To find the median of the given dataset, arrange it in ascending order.
Therefore, the dataset is 2, 3, 4, 6 and 7.
In this case, the number of observations is odd. (i.e) n= 5
Hence, median = (n+1)/2 th observation.
Median = (5+1)/2 = 6/2 = 3rd observation.
Therefore, the median of the given dataset is 4.
In a grouped data, it is not possible to find the median for the given observation by looking at the cumulative frequencies. The middle value of the given data will be in some class interval. So, it is necessary to find the value inside the class interval that divides the whole distribution into two halves. In this scenario, we have to find the median class.
To find the median class, we have to find the cumulative frequencies of all the classes and n/2. After that, locate the class whose cumulative frequency is greater than (nearest to) n/2. The class is called the median class.
After finding the median class, use the below formula to find the median value.
l is the lower limit of the median class
n is the number of observations
f is the frequency of median class
h is the class size
cf is the cumulative frequency of class preceding the median class.
Now, let us understand how to find the median of a grouped data using the formula with the help of an example.
The following data represents the survey regarding the heights (in cm) of 51 girls of Class x. Find the median height.
To find the median height, first, we need to find the class intervals and their corresponding frequencies.
The given distribution is in the form of being less than type,145, 150 …and 165 gives the upper limit. Thus, the class should be below 140, 140-145, 145-150, 150-155, 155-160 and 160-165.
From the given distribution, it is observed that,
4 girls are below 140. Therefore, the frequency of class intervals below 140 is 4.
11 girls are there with heights less than 145, and 4 girls with height less than 140
Hence, the frequency distribution for the class interval 140-145 = 11-4 = 7
Likewise, the frequency of 145 -150= 29 – 11 = 18
Frequency of 150-155 = 40-29 = 11
Frequency of 155 – 160 = 46-40 = 6
Frequency of 160-165 = 51-46 = 5
Therefore, the frequency distribution table along with the cumulative frequencies are given below:
Here, n= 51.
Therefore, n/2 = 51/2 = 25.5
Thus, the observations lie between the class interval 145-150, which is called the median class.
Lower class limit = 145
Class size, h = 5
Frequency of the median class, f = 18
Cumulative frequency of the class preceding the median class, cf = 11.
We know that the formula to find the median of the grouped data is:
Now, substituting the values in the formula, we get
Median = 145 + (72.5/18)
Median = 145 + 4.03
Median = 149.03.
Therefore, the median height for the given data is 149. 03 cm.
- Look at the last point on the far right of your graph. Its y-value is the total cumulative frequency, which is the number of points in the data set.
- Multiply this value by ½ and find it on the y-axis.
- Find the point on the line graph at this y-value.
- Find the x-axis at this point.
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