Cumulative frequency

Cumulative frequency is a concept used in statistics to summarize and analyze data by aggregating frequencies in a cumulative manner. It provides a running total of frequencies up to a certain point in a dataset, which is particularly useful for understanding the distribution of data and performing various statistical analyses.

### **Concept and Calculation**

1. **Definition**:

  Cumulative frequency represents the total number of data points that fall within or below a particular value or class interval in a frequency distribution. It helps in identifying how the frequency accumulates as you move through the data.

2. **Calculation**:

  To calculate cumulative frequency, follow these steps:

  - **Step 1**: Start with the first frequency value and write it down as the first cumulative frequency.

  - **Step 2**: Add the next frequency value to the cumulative frequency from the previous step.

  - **Step 3**: Continue this process for all frequency values.

### **Example**

Consider a dataset of scores with the following frequency distribution:

| Score Range | Frequency |

|------------- |-------- ---|

| 0 - 10    | 5      |

| 11 - 20    | 8       |

| 21 - 30    | 12     |

| 31 - 40    | 7      |

**Calculate the Cumulative Frequency:**

1. **For the range 0 - 10**:

  - Cumulative Frequency = 5

2. **For the range 11 - 20**:

  - Cumulative Frequency = 5 (previous cumulative) + 8 = 13

3. **For the range 21 - 30**:

  - Cumulative Frequency = 13 (previous cumulative) + 12 = 25

4. **For the range 31 - 40**:

  - Cumulative Frequency = 25 (previous cumulative) + 7 = 32

**Cumulative Frequency Table:**

| Score Range | Frequency | Cumulative Frequency |

|----------- --|--------- --|----------- -----------|

| 0 - 10    | 5      | 5           |

| 11 - 20    | 8      | 13           |

| 21 - 30    | 12     | 25           |

| 31 - 40    | 7      | 32           |

### **Applications**

1. **Creating Cumulative Frequency Distribution Tables**:

  Helps in summarizing data and visualizing the frequency distribution.

2. **Constructing Ogive Curves**:

  The cumulative frequency is used to plot an ogive, which is a graph that shows the cumulative frequency distribution.

3. **Data Analysis**:

  Cumulative frequency helps in understanding how data accumulates over intervals, which is useful for calculating percentiles, quartiles, and other statistical measures.

4. **Decision Making**:

  Provides insights into data trends and patterns, aiding in better decision-making in various fields such as economics, business, and social sciences.

By using cumulative frequency, you can gain a clearer picture of data distribution and make more informed analyses and decisions.

Hope this'll help.