The following table shows the results (70%) of 230 students in introduction to statistics (AMU-2011 E.C). The median and mode of the results are 33.5 and 34 respectively.
Marks
Number of students
0-9
4
10-19
16
20-29
f3
30-39
f4
40-49
f5
50-59
6
60-69
4
Determine the following
The missing frequencies
To determine the missing frequencies, we need to first calculate the total number of students who scored between 20-29 and 30-39.
From the given information, we know that the median score is 33.5. This means that 50% of the students scored below 33.5 and 50% scored above it.
Since the median is between the scores of 30-39, we can assume that 50% of the students scored between these two ranges. Therefore, the total number of students between 30-39 is half of the total number of students, which is 230/2 = 115.
Now, let's calculate the total number of students who scored between 20-29. We know that the mode score is 34, which means that the highest number of students scored 34.
From the given table, we can see that the number of students who scored 40-49, 50-59, and 60-69 is 5, 6, and 4 respectively. Since the mode is 34, the lowest score where the highest number of students scored, these scores are above it.
Therefore, we can assume that the total number of students who scored between 20-29 is the sum of these three numbers, which is 5 + 6 + 4 = 15.
Now, we know that the total number of students between 20-29 and 30-39 is 15 + 115 = 130.
To find the missing frequencies, we subtract the number of students in each score range from this total, and then divide by 10, since each frequency class represents a range of 10 marks.
For the 20-29 score range: Missing frequency = (130 - 15) / 10 = 11
For the 30-39 score range: Missing frequency = (130 - 115) / 10 = 1
So, the missing frequencies are 11 for the 20-29 score range and 1 for the 30-39 score range.