Answer :
To find the interval in which the median is located from the frequency table, follow these steps:
First, let's understand what the table provides:
- Grades with intervals and frequency:
- Grade A: $90-100$, Frequency: 3
- Grade B: $80-89$, Frequency: 5
- Grade C: $70-79$, Frequency: 8
- Grade D: $60-69$, Frequency: 4
- Grade F: $50-59$, Frequency: 2
The median of a dataset is the middle value when the numbers are arranged in order. If there's an even number of data points, the median is the average of the two middle numbers.
Step-by-step process to find in which interval the median is located:
Calculate the total frequency:
Total frequency = 3 + 5 + 8 + 4 + 2 = 22
Since the total frequency is 22, the median will be the average of the 11th and 12th data points.
Identify the interval that contains the 11th and 12th data points:
- Cumulative frequency up to Grade F ($50-59$) = 2.
- Cumulative frequency up to Grade D ($60-69$) = 2 + 4 = 6.
- Cumulative frequency up to Grade C ($70-79$) = 6 + 8 = 14.
The cumulative frequency of 14 for Grade C indicates that this interval contains the 11th and 12th data points.
Therefore, the median is located in the interval $70-79$.
The correct multiple-choice option is:
B. $70-79$
This process ensures the median is correctly identified within the given data, making it accessible and clear for anyone learning about finding medians in frequency tables.
