Final answer:
To find the median observations in the ordered frequency distribution, we calculate the total number of students and locate the middle observations, which are the 81st and 82nd values that correspond to a mark of 38.
Step-by-step explanation:
The question asks to find the median observations in a given frequency distribution where the marks are ordered. To find the median, we must first determine the total number of observations by adding the frequencies, and then locate the middle observations.
Here's a summary of the given data:
- 20 marks - 6 students
- 25 marks - 20 students
- 28 marks - 24 students
- 29 marks - 28 students
- 33 marks - 15 students
- 38 marks - 44 students
- 42 marks - 24 students
- 43 marks - 1 student
To find the total number of students, we add the number of students in each group:
6 + 20 + 24 + 28 + 15 + 44 + 24 + 1 = 162 students in total.
Since the number of observations is even, the median will be the average of the 81st and 82nd values. We can use a cumulative frequency table to locate these values. The 81st and 82nd values fall within the marks obtained by 38 students since the cumulative frequency just before 38 marks is 73 (6 + 20 + 24 + 28 - 1 = 73) and the cumulative frequency after including the 38 marks group is 117 (73 + 44 = 117).
Therefore, the 81st and 82nd observations, which are the median observations, correspond to the mark of 38.