Question

Find the median class for the following data.
Class 20 - 40 40 – 60 60 - 80 80-100
frequency 10 12 20 22​

Answer 1

Answer:

The correct answer is Class 80-100.

Step-by-step explanation:

Follow the steps given below in order to find the Median Class.

Since the class and frequency are given,

1.) Make a table and calculate the cumulative frequency as shown in the image.

2.) Let the Cumulative Frequency be N.

Here, the CF = 142.

3.) Divide the Cumulative Frequency by 2.

N/2 = 71

4.) Find the class corresponding to the Cumulative Frequency greater than N/2.

Class 80-100 contains the Cumulative Frequency = 142 which is greater 71.

5.) Such class is called Median class.

Hence, Class 80-100 is the Median Class.

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Answer 2

Answer:

The median class for the given data is 60-80, which contains the middle values of the dataset.

Step-by-step explanation:

To find the median class for the given data, we first need to determine the cumu lative frequency of each class interval.

Class Interval   Frequ ency Cumulative Frequency

20-40                      10                          10

40-60                      12                          22

60-80                     20                          42

80-100                    22                          64

The median class is the class interval that contains the median value of the data. To find the median value, we need to first calculate the total nu mber of obser vations in the dataset.

Total frequency = 10 + 12 + 20 + 22 = 64

Since the total frequency is even, the median value will be the average of the two middle values. The middle values are the 32nd and 33rd observations in the dataset.

To find the class interval that contains the 32nd and 33rd observations, we need to look at the cumulative frequency column. The 32nd observation falls within the 60-80 class inter val since the cumulative frequency up to and including this interval is 42. Therefore, the median class is the 60-80 class interval.

In summary , the median class for the given data is 60-80, which contains the middle values of the dataset. This indicates that 50% of the observations fall within this class interval.

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