Arithmetic Mean or Median of Arithmetic Progression (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise

TL;DR

The mean and median of evenly spaced numbers are equal and can be quickly found by averaging the first and last terms.

Transcript

2 3 4 and 7 how do we find the arithmetic mean and the median of this set of numbers there is no pattern in this set of numbers using the traditional approach we can find the mean with the formula sum of terms divided by the number of terms the sum of terms would be 2 + 3 + 4 + + 7 and the number of terms is 4 this will be 16 / 4 which equals 4 the... Read More

Key Insights

• 🍉 The arithmetic mean can be found by dividing the sum of the terms by the number of terms.
• 🍉 The median of a set with an even number of terms can be found by averaging the two middle terms.
• 👾 For evenly spaced numbers, the mean and median will always be equal.
• 👾 The mean and median of evenly spaced numbers can be quickly found by averaging the first and last terms.
• 😫 This concept is important for understanding the relationship between mean and median in different sets of numbers.
• 👾 The traditional approach is more time-consuming for finding the mean and median of evenly spaced numbers.
• 🍉 Using the average of the first and last terms is a simple and efficient method for finding the mean and median.

Questions & Answers

Q: How do we find the arithmetic mean and median of a set of numbers without a pattern?

The arithmetic mean can be found by dividing the sum of the terms by the number of terms. The median can be found by averaging the two middle terms if the number of terms is even.

Q: Can the mean and median be different for evenly spaced numbers?

No, for evenly spaced numbers, the mean and median will always be equal.

Q: How do we find the mean and median of evenly spaced numbers?

For evenly spaced numbers, both the mean and median can be found by averaging the first and last terms.

Q: Why is it quicker to find the mean and median of evenly spaced numbers using this method?

It is quicker because there is no need to add up all the numbers or calculate the middle value - just average the first and last terms.

Summary & Key Takeaways

• The arithmetic mean of a set of numbers can be found by dividing the sum of the terms by the number of terms.

• The median of a set of numbers with an even number of terms can be found by averaging the two middle terms.

• For evenly spaced numbers, both the mean and median can be found by averaging the first and last terms.