Answer :
To find the interval where the median is located, we need to follow a series of steps based on the data provided in the frequency table.
1. Understand the Frequency Table:
- You have different grade intervals: 90-100, 80-89, 70-79, 60-69, 50-59.
- Each interval has a frequency which tells us how many values fall into that range.
2. Calculate the Total Number of Observations:
- Add up all the frequencies:
[tex]\[
3 (for \, 90-100) + 5 (for \, 80-89) + 8 (for \, 70-79) + 4 (for \, 60-69) + 2 (for \, 50-59) = 22
\][/tex]
- So, there are 22 observations in total.
3. Determine the Median Position:
- The median is the middle value. For 22 observations, the median position is:
[tex]\[
\frac{22}{2} = 11
\][/tex]
- This means the median is between the 11th and 12th observation.
4. Locate the Interval of the Median:
- We will add up the frequencies until we reach or exceed the middle position, which is the 11th observation.
- Cumulative Frequency:
- Start from the lowest interval and move upwards:
- 50-59: cumulative frequency = 2
- 60-69: cumulative frequency = 2 + 4 = 6
- 70-79: cumulative frequency = 6 + 8 = 14
- At the interval 70-79, the cumulative frequency reaches 14, which includes the 11th observation.
Therefore, the median is located in the interval 70-79.
1. Understand the Frequency Table:
- You have different grade intervals: 90-100, 80-89, 70-79, 60-69, 50-59.
- Each interval has a frequency which tells us how many values fall into that range.
2. Calculate the Total Number of Observations:
- Add up all the frequencies:
[tex]\[
3 (for \, 90-100) + 5 (for \, 80-89) + 8 (for \, 70-79) + 4 (for \, 60-69) + 2 (for \, 50-59) = 22
\][/tex]
- So, there are 22 observations in total.
3. Determine the Median Position:
- The median is the middle value. For 22 observations, the median position is:
[tex]\[
\frac{22}{2} = 11
\][/tex]
- This means the median is between the 11th and 12th observation.
4. Locate the Interval of the Median:
- We will add up the frequencies until we reach or exceed the middle position, which is the 11th observation.
- Cumulative Frequency:
- Start from the lowest interval and move upwards:
- 50-59: cumulative frequency = 2
- 60-69: cumulative frequency = 2 + 4 = 6
- 70-79: cumulative frequency = 6 + 8 = 14
- At the interval 70-79, the cumulative frequency reaches 14, which includes the 11th observation.
Therefore, the median is located in the interval 70-79.
