A frequency distribution is a summary of data that shows the number of observations (frequency) in each category or interval. It functions as a method to systematically arrange and present unprocessed data in a meaningful way, facilitating analysis and the derivation of conclusions. Widely applied in statistics, frequency distributions provide a descriptive overview of the spread of values within a dataset.
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Here’s are key components of frequency distribution:
Categories or intervals: These are the groups or ranges into which the data is divided. For example, in a dataset of weight based on age, categories could be weight ranges like 0-10, 11-20, 20-30 and so on. Frequency : The frequency of a category denotes the count of observations or data points situated within that specific category, indicating the frequency with which a particular value or range appears in the dataset.
Cumulative Frequency: Cumulative frequency is the running total of frequencies as you move through the categories. It helps in understanding the total number of observations up to a certain point in the distribution.
Relative Frequency: Relative frequency is the proportion of observations in a category relative to the total number of observations. It is calculated by dividing the frequency of a category by the total number of observations.
Here’s a simple example to illustrate the concept:
Suppose you have a dataset of exam scores for a class of students:
To create a frequency distribution, you would organize the data and count the occurrences of each score:
| Score Range(categories or intervals) | Frequency | Cumulative Frequency | Relative Frequency |
|---|---|---|---|
| 0-10 | 6 | 6 | 6/4=1.5 |
| 10-20 | 2 | 6+2=8 | 2/4=0.5 |
| 20-30 | 2 | 8+2=10 | 2/4=0.5 |
| 30-40 | 4 | 10+4=14 | 4/4=1 |
Looking at the table above, can you understand what each of the columns means?