Median Of Grouped Data

The cumulative frequencies are:

50-70: 15 50-90: 15+21 = 36
50-110: 36+32 = 68
50-130: 68+19 = 87
50-150: 87+8 = 95
50-170: 95+5 = 100

The total number of observations is 100.

The median is the value such that half the observations are below it and half are above it.

Since there are 100 observations, the median will be the average of the 50th and 51st observations.

The cumulative frequency tells us the number of observations below the upper limit of each class.

The 50th and 51st observations will lie in the class interval 90-110 since the cumulative frequency of the 50-90 class is 36, and the cumulative frequency of the 50-110 class is 68.

So the median class is 90-110. The upper limit of the median class is 110.

Step 1: Formula for Mode for Grouped Data.
The formula for finding the mode for grouped data is: where:
is the lower boundary of the modal class,
is the frequency of the modal class,
is the frequency of the class preceding the modal class,
is the frequency of the class succeeding the modal class,
is the class width.
Step 2: Understanding the Formula.
This formula helps us find the mode when the data is grouped into class intervals. The mode is adjusted based on the frequencies of the modal class and its neighboring classes.
Step 3: Conclusion.
Thus, the correct formula for finding the mode for grouped data is: