From The Given Data, Answer The Following Questions:$\[ \begin{tabular}{|l|l|l|l|l|l|} \hline \text{Class Interval:} & 25 & 35 & 45 & 55 & 65 \\ \hline \text{Frequency:} & 8 & 16 & 4 & 4 & 3 \\ \hline \end{tabular} \\]a) If Data Has

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Introduction

In mathematics, frequency distribution is a table that displays the frequency of different values in a dataset. It is a powerful tool used to summarize and analyze large datasets. In this article, we will explore the given frequency distribution data and answer the questions posed.

The Given Frequency Distribution Data

Class Interval: 25 35 45 55 65
Frequency: 8 16 4 4 3

Question 1: Understanding the Frequency Distribution

The given frequency distribution data represents the frequency of different class intervals in a dataset. The class intervals are the ranges of values, and the frequency is the number of times each value occurs in the dataset.

  • Class Interval 25: This class interval represents values between 25 and 35 (inclusive). The frequency of 8 indicates that there are 8 values in the dataset that fall within this range.
  • Class Interval 35: This class interval represents values between 35 and 45 (inclusive). The frequency of 16 indicates that there are 16 values in the dataset that fall within this range.
  • Class Interval 45: This class interval represents values between 45 and 55 (inclusive). The frequency of 4 indicates that there are 4 values in the dataset that fall within this range.
  • Class Interval 55: This class interval represents values between 55 and 65 (inclusive). The frequency of 4 indicates that there are 4 values in the dataset that fall within this range.
  • Class Interval 65: This class interval represents values between 65 and 75 (inclusive). The frequency of 3 indicates that there are 3 values in the dataset that fall within this range.

Question 2: Calculating the Total Frequency

To calculate the total frequency, we need to add up the frequencies of all the class intervals.

Total Frequency = 8 + 16 + 4 + 4 + 3 Total Frequency = 35

The total frequency represents the total number of values in the dataset.

Question 3: Calculating the Class Width

The class width is the difference between the upper and lower class limits. In this case, the class width is the difference between the upper and lower class limits of each class interval.

Class Width = (Upper Class Limit - Lower Class Limit) Class Width = (35 - 25) = 10 Class Width = (45 - 35) = 10 Class Width = (55 - 45) = 10 Class Width = (65 - 55) = 10

The class width is 10 for all class intervals.

Question 4: Calculating the Mid-Point of Each Class Interval

The mid-point of each class interval is the average of the upper and lower class limits.

Mid-Point = (Upper Class Limit + Lower Class Limit) / 2 Mid-Point = (25 + 35) / 2 = 30 Mid-Point = (35 + 45) / 2 = 40 Mid-Point = (45 + 55) / 2 = 50 Mid-Point = (55 + 65) / 2 = 60

The mid-points of each class interval are 30, 40, 50, and 60.

Conclusion

In this article, we have analyzed the given frequency distribution data and answered the questions posed. We have calculated the total frequency, class width, and mid-point of each class interval. The frequency distribution data is a powerful tool used to summarize and analyze large datasets. By understanding and analyzing frequency distribution data, we can gain insights into the underlying patterns and trends in the data.

Frequently Asked Questions

Q: What is frequency distribution data?

A: Frequency distribution data is a table that displays the frequency of different values in a dataset.

Q: How do I calculate the total frequency?

A: To calculate the total frequency, you need to add up the frequencies of all the class intervals.

Q: What is the class width?

A: The class width is the difference between the upper and lower class limits.

Q: How do I calculate the mid-point of each class interval?

A: To calculate the mid-point of each class interval, you need to average the upper and lower class limits.

References

Glossary

  • Frequency Distribution: A table that displays the frequency of different values in a dataset.
  • Class Interval: A range of values in a dataset.
  • Frequency: The number of times a value occurs in a dataset.
  • Class Width: The difference between the upper and lower class limits.
  • Mid-Point: The average of the upper and lower class limits.
    Frequently Asked Questions About Frequency Distribution Data ====================================================================

Q: What is frequency distribution data?

A: Frequency distribution data is a table that displays the frequency of different values in a dataset. It is a powerful tool used to summarize and analyze large datasets.

Q: How do I create a frequency distribution table?

A: To create a frequency distribution table, you need to follow these steps:

  1. Collect the data: Gather the data you want to analyze.
  2. Determine the class intervals: Divide the data into class intervals or ranges.
  3. Count the frequency: Count the number of times each value occurs in the dataset.
  4. Create the table: Create a table with the class intervals as the rows and the frequency as the columns.

Q: What is the purpose of frequency distribution data?

A: The purpose of frequency distribution data is to summarize and analyze large datasets. It helps to identify patterns, trends, and relationships in the data.

Q: How do I calculate the total frequency?

A: To calculate the total frequency, you need to add up the frequencies of all the class intervals.

Q: What is the class width?

A: The class width is the difference between the upper and lower class limits.

Q: How do I calculate the mid-point of each class interval?

A: To calculate the mid-point of each class interval, you need to average the upper and lower class limits.

Q: What is the difference between a frequency distribution table and a histogram?

A: A frequency distribution table is a table that displays the frequency of different values in a dataset, while a histogram is a graphical representation of the frequency distribution data.

Q: How do I use frequency distribution data to analyze a dataset?

A: To use frequency distribution data to analyze a dataset, you need to follow these steps:

  1. Examine the frequency distribution table: Look for patterns, trends, and relationships in the data.
  2. Calculate the mean and median: Calculate the mean and median of the dataset to get an idea of the central tendency.
  3. Calculate the mode: Calculate the mode of the dataset to get an idea of the most frequently occurring value.
  4. Calculate the range: Calculate the range of the dataset to get an idea of the spread of the data.

Q: What are the advantages of using frequency distribution data?

A: The advantages of using frequency distribution data include:

  • It helps to summarize and analyze large datasets.
  • It helps to identify patterns, trends, and relationships in the data.
  • It helps to calculate the mean, median, mode, and range of the dataset.

Q: What are the disadvantages of using frequency distribution data?

A: The disadvantages of using frequency distribution data include:

  • It can be time-consuming to create a frequency distribution table.
  • It can be difficult to interpret the data if the class intervals are too wide or too narrow.
  • It can be difficult to calculate the mean, median, mode, and range of the dataset if the data is skewed or has outliers.

Conclusion

In this article, we have answered some of the frequently asked questions about frequency distribution data. We have discussed the purpose of frequency distribution data, how to create a frequency distribution table, and how to use frequency distribution data to analyze a dataset. We have also discussed the advantages and disadvantages of using frequency distribution data.

References

Glossary

  • Frequency Distribution: A table that displays the frequency of different values in a dataset.
  • Class Interval: A range of values in a dataset.
  • Frequency: The number of times a value occurs in a dataset.
  • Class Width: The difference between the upper and lower class limits.
  • Mid-Point: The average of the upper and lower class limits.
  • Mean: The average of a dataset.
  • Median: The middle value of a dataset.
  • Mode: The most frequently occurring value in a dataset.
  • Range: The difference between the highest and lowest values in a dataset.