Impact on median and mean when removing lowest value example | 6th grade | Khan Academy

TL;DR

Removing the lowest score increases both the mean and median, with the mean increasing by a greater amount.

Transcript

• "Ana played five rounds of golf "and her lowest score was an 80. " The scores of the first four rounds and the lowest round "are shown in the following dot plot." And we see it right over here. The lowest round she scores an 80, she also scores a 90 once, a 92 once, a 94 once, and a 96 once. "It was discovered that Ana broke some rules when she s... Read More

Key Insights

• 😘 Removing the lowest score increased both the mean and median.
• ❓ The median increased by 1, while the mean increased from 90.4 to 93.
• 😘 Removing a lower score increases the mean due to the elimination of a low value dragging down the average.
• 💯 Removing a lower score increases the median because the remaining scores are closer together.
• 💯 Cheating by scoring an 80 did not benefit Ana as the score was removed, and the mean and median increased regardless.

Questions & Answers

Q: How does removing the lowest score impact the median and mean in this scenario?

Removing the lowest score increases both the median and mean. The median increased by 1, while the mean increased from 90.4 to 93.

Q: Why does removing a lower score increase the mean?

Removing a lower score raises the mean because the low value no longer contributes to the average calculation. Without the lower score, the remaining scores have a higher total sum, increasing the mean.

Q: Why does removing a lower score increase the median?

Removing a lower score increases the median because the remaining scores are now closer together. When calculating the median of an even number of values, the average of the middle two values is taken. Removing the lower score brings the remaining scores closer, resulting in a higher value for the median.

Q: How does cheating and removing the lowest score affect the analysis?

Cheating by scoring an 80 initially did not help Ana because the score was removed. Removing the lowest score had the impact of increasing both the mean and median, demonstrating that cheating does not necessarily improve performance.

Summary & Key Takeaways

• Ana played five rounds of golf with scores of 80, 90, 92, 94, and 96.

• The lowest score of 80 was removed due to breaking rules.

• Prior to removal, the median score was 92, and the mean score was 90.4.

• After removal, the median score increased to 93, and the mean score increased to 93.