Impact on median and mean when increasing highest value | 6th grade | Khan Academy

TL;DR

Increasing a high score in a dataset does not affect the median, but it increases the mean.

Transcript

• [Voiceover] Let's think about what happens to the median and mean of a set of numbers when I change one of the numbers. And so let's look at this example. A group of four friends likes to bowl together, and each friend keeps track of his all-time highest score in a single game. Their high scores are all between 180 and 220, except for Adam, whose... Read More

Key Insights

• #️⃣ The median remains unchanged when a single number in a dataset is changed, as long as the position of that number in the order remains the same.
• ✋ The mean increases when a higher value is introduced into the dataset because it affects the sum of all the numbers.
• 🇨🇫 The median is a measure of central tendency that is less influenced by extreme values, while the mean considers all values equally.
• 🛀 The concept can be visualized by replacing the undefined value with a specific number, showing that the median does not change but the mean does.

Questions & Answers

Q: How does increasing Adam's high score affect the median and mean of the dataset?

Increasing Adam's high score does not affect the median because the median is calculated based on the middle two numbers, which remain unchanged. However, the mean increases because the higher score increases the sum of all the numbers in the dataset.

Q: What is the difference between the median and the mean?

The median is the middle number in a dataset, whereas the mean is the average of all the numbers in the dataset. The median is not affected by extreme values, but the mean is influenced by all the values in the dataset.

Q: Why does increasing the highest score affect the mean?

Increasing the highest score affects the mean because the mean is calculated by summing up all the numbers and dividing by the total count. When the highest score increases, the sum of all the numbers also increases, leading to a higher mean.

Q: Can you provide an example of a dataset where the median and mean would be different?

Let's say we have the following dataset: 10, 20, 30, 40, 50. The median would be 30 because it's the middle number, while the mean would be 30 because it's the sum of all the numbers (150) divided by the total count (5).

Summary & Key Takeaways

• A group of friends keep track of their high scores in bowling, with all scores ranging from 180 to 220, except for Adam whose high score is 250.

• After Adam achieves a new high score of 290, the dataset remains the same except for Adam's score, which increases.

• The median, which is the middle number, remains unchanged because the two middle numbers in the dataset remain the same.

• However, the mean, which is the average of all numbers, increases because the sum of all the numbers increases with the higher score.