Find the median of the following series: Size: 20, 25, 30, 35, 40, 45, 50, 55 Frequency: 14, 18, 33, 30, 20, 15, 13, 7
Understand the Problem
The question asks to find the median of a given frequency distribution. The data is presented in a table format with sizes and their corresponding frequencies. We need to calculate the cumulative frequencies, identify the median class, and then apply the median formula.
Answer
$M = 35$
Answer for screen readers
$M = 35$
Steps to Solve
-
Calculate Cumulative Frequencies
- Add the frequencies cumulatively to obtain the cumulative frequencies.
- The cumulative frequencies are:
- 20: 14
- 25: 14 + 18 = 32
- 30: 32 + 33 = 65
- 35: 65 + 30 = 95
- 40: 95 + 20 = 115
- 45: 115 + 15 = 130
- 50: 130 + 13 = 143
- 55: 143 + 7 = 150
-
Determine the Median Position
- Calculate $N/2$, where $N$ is the total frequency. In this case, $N = 150$.
- $N/2 = 150 / 2 = 75$
-
Identify the Median Class
- Find the cumulative frequency that is just greater than or equal to $N/2 = 75$.
- The cumulative frequency 95 (corresponding to size 35) is the first one greater than 75.
- Therefore, the median class is 35.
-
Determine the Median Since we're dealing with discrete data, the median is simply the size corresponding to the cumulative frequency that exceeds $N/2$. In this case, the median is 35.
$M = 35$
More Information
The median is the middle value of a dataset. In a frequency distribution, it's the value that splits the distribution into two equal halves.
Tips
A common mistake is to incorrectly calculate the cumulative frequencies. Ensure that you are adding the frequencies correctly. Another mistake is to confuse frequency with cumulative frequency when determining which size corresponds to the median.
AI-generated content may contain errors. Please verify critical information
