Prepare GAT General in 21 Days- Day 3/Lecture-3| Averages and Time & Work

Averaging and Statistical Calculations
📌 The core of the session involves calculating the average (arithmetic mean) using the fundamental formula: $\text{Average} = \frac{\text{Sum of elements}}{\text{Number of elements}}$.
📌 Calculations were demonstrated for finding a missing score when the average of the initial tests and the final average are known, such as determining a required score of 95 in the fifth test to achieve an average of 84 across five tests, given the initial average was 80 for four tests.
📌 Applied the average formula to find the total sum when the average and count are known; for example, if 25 students have an average score of 62, the total score is $25 \times 62 = 1550$.

Application of Averages in Speed and Work Problems
🏎️ Solved a problem requiring the calculation of average speed using the formula: $\text{Average Speed} = \frac{\text{Total Distance Covered}}{\text{Total Time Taken}}$.
⚙️ Solved a "work and time" problem where the combined time taken by two entities (A and B) working together was used to determine the time taken by each entity individually, leveraging the relationship $1/A + 1/B = 1/\text{Total Time}$.

Finding Median and Power Calculations
📊 The concept of the Median was introduced: for an odd number of elements, it's the middle element; for an even number, it's the average of the two middle elements.
🧮 Calculated the arithmetic mean for terms involving powers, confirming that the arithmetic mean of $2^8$ and $2^{10}$ is $2^8\sqrt{5}$.

Key Points & Insights
➡️ Master the basic average formula ($\text{Sum} = \text{Average} \times \text{Count}$) as it is the key to solving diverse quantitative problems involving scores, speed, and accumulated values.
➡️ When dealing with speed problems, always ensure you use Total Distance divided by Total Time to find the true Average Speed, not just the average of different speeds.
➡️ For work and time problems, use the reciprocal relationship ($1/A + 1/B = 1/T_{\text{total}}$) to efficiently calculate combined completion rates.

📸 Video summarized with SummaryTube.com on Feb 24, 2026, 05:53 UTC