Class 9 Mathematic Statistics All Formula & Concept Notes | Formula Sheet

here's a detailed overview of the formulas and concepts in Statistics for Class 9 Mathematics:

1. Introduction to Statistics

• Statistics: The science of collecting, analyzing, presenting, and interpreting data.

2. Types of Data

• Qualitative Data: Non-numerical data (e.g., colors, names).
• Quantitative Data: Numerical data (e.g., height, weight).

3. Data Collection

• Primary Data: Data collected directly from the source (e.g., surveys, experiments).
• Secondary Data: Data collected from existing sources (e.g., books, articles).

4. Organizing Data

• Raw Data: The initial set of data collected.
• Tally Marks: A way to count data visually.
• Frequency Distribution Table: A table that shows the number of occurrences of each value.

5. Measures of Central Tendency

• Mean (Average): The sum of all data values divided by the number of values.

  Formula:

  $$\text{Mean} = \frac{\sum x_i}{N}$$

  where $\sum x_i$ is the sum of all data values and $N$ is the number of values.

• Median: The middle value when the data is arranged in ascending or descending order.

  • For an odd number of observations: The median is the middle value.
  • For an even number of observations: The median is the average of the two middle values.

• Mode: The value that occurs most frequently in the data set.

6. Measures of Dispersion

• Range: The difference between the highest and lowest values.

  Formula:

  $$\text{Range} = \text{Highest value} - \text{Lowest value}$$

• Variance: The average of the squared differences from the Mean.

  Formula:

  $$\text{Variance} = \frac{\sum (x_i - \text{Mean})^2}{N}$$

• Standard Deviation: The square root of the variance. It provides a measure of how spread out the data values are around the mean.

  Formula:

  $$\text{Standard Deviation} = \sqrt{\text{Variance}}$$
  

7. Graphical Representation of Data

• Bar Graph: A chart that uses bars to show the frequency of each category.
• Histogram: A bar graph where the bars represent the frequency of data within intervals (bins).
• Pie Chart: A circular chart divided into sectors, each representing a proportion of the whole.
• Frequency Polygon: A line graph that shows the frequencies of different intervals.

8. Probability

• Probability: The measure of the likelihood that an event will occur.

  Formula:

  $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$

9. Cumulative Frequency

• Cumulative Frequency: The running total of frequencies up to a certain point in a data set.

  • Cumulative Frequency Table: A table that shows the cumulative frequency for each class interval.

10. Ogive

• Ogive: A graph that represents the cumulative frequency of a data set. It can be used to determine the number of observations below a particular value.