The following table shows marks secured by 140 students in an examination: Marks 0-10 10-20 20-30 30-40 40-50 Number 20 of 24 40 36 20 students Calculate mean marks by using all the three methods, i.e., dire X od, assumed mean method and step-deviation method.

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### Statistical Analysis of Examination Marks

#### Table of Marks Secured by 140 Students

The following table displays the distribution of marks secured by 140 students in an examination. The marks are divided into five intervals, and the number of students for each interval is provided.

| Marks  | Number of Students |
|--------|--------------------|
| 0-10   | 20                 |
| 10-20  | 24                 |
| 20-30  | 40                 |
| 30-40  | 36                 |
| 40-50  | 20                 |

#### Calculation Task

Calculate the mean marks by using the following three methods:

1. **Direct Method:** This involves using the formula for the mean of a frequency distribution.
2. **Assumed Mean Method:** This method simplifies the calculations by assuming a mean value, typically the midpoint of one of the intervals.
3. **Step-Deviation Method:** This method is used when the data intervals are regular and simplifies calculations by reducing the size of the numbers involved.

The calculations aid in understanding different statistical methods and comparing their ease and effectiveness in practical scenarios. These methods are beneficial in educational settings for teaching students how to analyze data in various ways.
Transcribed Image Text:### Statistical Analysis of Examination Marks #### Table of Marks Secured by 140 Students The following table displays the distribution of marks secured by 140 students in an examination. The marks are divided into five intervals, and the number of students for each interval is provided. | Marks | Number of Students | |--------|--------------------| | 0-10 | 20 | | 10-20 | 24 | | 20-30 | 40 | | 30-40 | 36 | | 40-50 | 20 | #### Calculation Task Calculate the mean marks by using the following three methods: 1. **Direct Method:** This involves using the formula for the mean of a frequency distribution. 2. **Assumed Mean Method:** This method simplifies the calculations by assuming a mean value, typically the midpoint of one of the intervals. 3. **Step-Deviation Method:** This method is used when the data intervals are regular and simplifies calculations by reducing the size of the numbers involved. The calculations aid in understanding different statistical methods and comparing their ease and effectiveness in practical scenarios. These methods are beneficial in educational settings for teaching students how to analyze data in various ways.
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