Activity 3: That's My PlaceDaily Allowance Of 60 Students$[ \begin{array}{|c|c|c|} \hline \text{Class Interval} & F & \ \textless \ Cf \ \hline 81-90 & 7 & 60 \ \hline 71-80 & 10 & 53 \ \hline 61-70 & 15 & 43 \ \hline 51-60 & 4 & 28
Activity 3: That's My Place - Understanding the Frequency Distribution of Daily Allowance
In this activity, we will be exploring the concept of frequency distribution and how it can be used to understand the daily allowance of 60 students. The frequency distribution is a table that displays the number of observations that fall within a particular range or interval. In this case, we will be using a frequency distribution table to understand the daily allowance of the students.
The Frequency Distribution Table
| Class Interval | f | <cf |
|---|---|---|
| 81-90 | 7 | 60 |
| 71-80 | 10 | 53 |
| 61-70 | 15 | 43 |
| 51-60 | 4 | 28 |
Understanding the Frequency Distribution
The frequency distribution table shows us the number of students who fall within each class interval. The class interval is the range of values that the daily allowance can take. For example, the first class interval is 81-90, which means that the daily allowance can take any value between 81 and 90. The frequency 'f' represents the number of students who fall within each class interval.
Calculating the Cumulative Frequency
The cumulative frequency '<cf' represents the total number of students who fall within each class interval and all the previous class intervals. For example, the cumulative frequency for the first class interval is 60, which means that 60 students have a daily allowance between 81 and 90. The cumulative frequency for the second class interval is 53, which means that 53 students have a daily allowance between 71 and 80, and 7 students have a daily allowance between 81 and 90.
Interpreting the Frequency Distribution
The frequency distribution table can be used to understand the distribution of daily allowance among the students. For example, we can see that the majority of the students (43) have a daily allowance between 61 and 70. This suggests that the daily allowance is skewed towards the lower end of the range. We can also see that there are fewer students (4) who have a daily allowance between 51 and 60.
Calculating the Mean and Median
To calculate the mean, we need to multiply each class interval by its frequency and add up the results. We then divide the sum by the total number of students.
Mean = (81-90 x 7) + (71-80 x 10) + (61-70 x 15) + (51-60 x 4) / 60 Mean = 567 + 710 + 975 + 204 / 60 Mean = 2456 / 60 Mean = 40.93
To calculate the median, we need to find the middle value of the data. Since there are 60 students, the median will be the 30th value.
| Class Interval | f | <cf |
|---|---|---|
| 81-90 | 7 | 60 |
| 71-80 | 10 | 53 |
| 61-70 | 15 | 43 |
| 51-60 | 4 | 28 |
The 30th value falls within the class interval 61-70. Therefore, the median is 65.
In this activity, we have explored the concept of frequency distribution and how it can be used to understand the daily allowance of 60 students. We have calculated the mean and median of the data and interpreted the frequency distribution table. The frequency distribution table shows us the number of students who fall within each class interval and can be used to understand the distribution of daily allowance among the students.
- What is the significance of the frequency distribution table in understanding the daily allowance of the students?
- How can the frequency distribution table be used to identify the mode of the data?
- What is the difference between the mean and median of the data?
- How can the frequency distribution table be used to understand the skewness of the data?
- The frequency distribution table is a graphical representation of the data and can be used to understand the distribution of the data.
- The cumulative frequency '<cf' represents the total number of students who fall within each class interval and all the previous class intervals.
- The mean and median are measures of central tendency and can be used to understand the distribution of the data.
- The frequency distribution table can be used to identify the mode of the data and understand the skewness of the data.
- The frequency distribution table can be used in real-world applications such as understanding the distribution of exam scores among students.
- The frequency distribution table can be used to understand the distribution of daily allowance among employees.
- The frequency distribution table can be used to understand the distribution of sales among products.
In conclusion, the frequency distribution table is a powerful tool that can be used to understand the distribution of data. It can be used to identify the mode of the data, understand the skewness of the data, and calculate the mean and median of the data. The frequency distribution table can be used in real-world applications such as understanding the distribution of exam scores among students, understanding the distribution of daily allowance among employees, and understanding the distribution of sales among products.
Frequently Asked Questions (FAQs) - Activity 3: That's My Place
A1: The frequency distribution table is a graphical representation of the data and can be used to understand the distribution of the daily allowance among the students. It shows the number of students who fall within each class interval and can be used to identify the mode of the data, understand the skewness of the data, and calculate the mean and median of the data.
A2: The mode of the data is the value that appears most frequently in the data. To identify the mode of the data, we need to look at the frequency distribution table and find the class interval with the highest frequency. In this case, the class interval 61-70 has the highest frequency of 15, which means that the mode of the data is 65.
A3: The mean and median are measures of central tendency and can be used to understand the distribution of the data. The mean is the average of the data and is calculated by multiplying each class interval by its frequency and adding up the results. The median is the middle value of the data and is calculated by finding the 30th value of the data. In this case, the mean is 40.93 and the median is 65.
A4: The skewness of the data is a measure of how symmetrical the data is. To understand the skewness of the data, we need to look at the frequency distribution table and see if the data is skewed to the left or right. In this case, the data is skewed to the right, which means that there are more students with higher daily allowances.
A5: Understanding the distribution of the data is important because it can be used to make informed decisions. For example, if the data is skewed to the right, it may indicate that there are more students with higher daily allowances, which can be used to inform decisions about budgeting and resource allocation.
A6: The frequency distribution table can be used in real-world applications such as understanding the distribution of exam scores among students, understanding the distribution of daily allowance among employees, and understanding the distribution of sales among products.
A7: Some common mistakes to avoid when working with frequency distribution tables include:
- Not understanding the concept of frequency distribution
- Not using the correct class intervals
- Not calculating the cumulative frequency correctly
- Not interpreting the results correctly
A8: The frequency distribution table can be used to identify outliers in the data by looking at the class intervals with the lowest frequencies. In this case, the class interval 51-60 has the lowest frequency of 4, which may indicate that there are outliers in the data.
A9: Some common applications of frequency distribution tables in business and economics include:
- Understanding the distribution of sales among products
- Understanding the distribution of daily allowance among employees
- Understanding the distribution of exam scores among students
- Understanding the distribution of customer demographics
A10: The frequency distribution table can be used to make informed decisions by providing a clear and concise representation of the data. It can be used to identify trends and patterns in the data, understand the distribution of the data, and make informed decisions about budgeting and resource allocation.