Statistics Lecture Notes

Introduction

• Welcome to the channel.
• We are completing a whole series on Statistics in 15 days.
• Previously, we have covered Correlation and Index Number.
• Today, we will discuss the Mean.
• Tomorrow is the Revision day.

What is Mean?

• Mean is a measure that helps to find the Average.
• We denote it as X bar (x̄).
• Mean can be shown in three types of Series:
  • Individual Series
  • Discrete Series
  • Continuous Series

Explanation of Series

1. Individual Series: Only X values are there (like 2, 4, 6, 8, 10).
2. Discrete Series: Both X and its Frequency are there.
3. Continuous Series: X has Class Intervals (like 0-5, 5-10).

Formulas to Calculate Mean

Individual Series

• There are three formulas to calculate the Mean:

  • Direct Method:

    [ x̄ = \frac{Σx}{N} ]

  • Shortcut Method:

    [ x̄ = A + \frac{ΣD}{N} ]

  • Step Deviation Method:

    [ x̄ = A + \frac{ΣD'}{N} \times C ]

Example Calculation (Direct Method)

• Given values: 120, 150, 180, 200, 250, 300, 220, 350, 370, 240
• Sum of total values: 2400
• Total terms (N): 10
• Mean = 2400 / 10 = 240

Shortcut Method Calculation

• Assume Mean (A): 120
• Calculate D: X - A
• Use the formula:
  [ D = X - A ]
• Mean = A + [ \frac{ΣD}{N} ]
• Result: Mean = 240

Calculate Mean for Discrete Series

• Direct Method:
  [ x̄ = \frac{Σfx}{Σf} ]
• Shortcut Method:
  [ x̄ = A + \frac{ΣFD}{ΣF} ]
• Given example, sum of 3500 and total count of 100. Mean = 35

Continuous Series

• In a Continuous Series, there is no X, only Class Intervals.
• Formula:
  [ x̄ = \frac{Σfm}{Σf} ]
  • M = Mid value (Lower limit + Upper limit / 2)
  • Calculate M and then compute FM.

Example Calculation (Continuous Series)

• Calculate Mid values and sum of FM.
• Finally, compute the Mean.

Conclusion

• All methods yield the same result for Mean.
• Homework: Write down and memorize all the formulas in one place.
• Be prepared for revision and review the previously learned topics.
• Thank you!