Health step recording and averages

[Rayzer]

The statement appears to contain a slight contradiction. 

Contradictory Statement

If you walked 629 fewer steps daily than the average for your age group, it would generally indicate that you are below the average, not above it. Being in the top 57% suggests that you are doing more than 43% of individuals in your age group. Therefore, if walking fewer steps places you in the top 57%, it could imply that the majority of people in your age group walk even fewer steps.

Please don't understand me; I'm not saying I don't like being above average.

[userZNnTdcqwZP · Accepted solution]

Here's some nerdy math

The average is NOT ALWAYS the 50th percentile (50%). The median is the 50th percentile.

You can be slightly below average but still above the median (50%) because the distribution for your age group is positively skewed or right-skewed.

[Rayzer]

You have provided the most excellent answer. I ran it through Copilot, and your spot on!

1. Average vs Median: The average (or mean) of a dataset is the sum of all values divided by the number of values. The median, on the other hand, is the middle value when the data is sorted in ascending order. If the dataset has an even number of observations, the median is the average of the two middle numbers. The median is indeed the 50th percentile, which means 50% of the observations fall below this value,
2. Average and Median in Skewed Distributions: In a perfectly symmetrical distribution, the average and median are the same. However, in skewed distributions, this is not the case. If a distribution is positively skewed (or right-skewed), it has a long tail on the right side. In such a distribution, the mean is typically greater than the median because the few high values pull the mean upward.
So, if you are slightly below average in a positively skewed distribution, you could still be above the median. This is because the average is influenced by the high values on the right tail, while the median is not. Therefore, your statement is accurate.