Question
\( 4,5,5,5,6,9,9,18,20 \) The mean is bigger than the median.
Ask by John Ellis. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The mean is 9 and the median is 6, so the mean is bigger than the median.
Solution
1. The given data in order is: \(4, 5, 5, 5, 6, 9, 9, 18, 20\).
2. There are 9 numbers in the data set. Since 9 is odd, the median is the middle number, which is the \(5^\text{th}\) value in the sorted list. Thus, the median is:
\[
\text{Median} = 6.
\]
3. To find the mean, calculate the sum of all the numbers:
\[
4 + 5 + 5 + 5 + 6 + 9 + 9 + 18 + 20 = 81.
\]
Since there are 9 numbers, the mean is:
\[
\text{Mean} = \frac{81}{9} = 9.
\]
4. Comparing the mean and the median:
\[
9 > 6.
\]
Thus, the mean is bigger than the median.
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Simplify this solution The Deep Dive
When examining the numbers \( 4, 5, 5, 5, 6, 9, 9, 18, 20 \), we first calculate the mean by summing them up: \( 4 + 5 + 5 + 5 + 6 + 9 + 9 + 18 + 20 = 81 \), and dividing by the total number of values, which is 9. This yields a mean of \( 9 \). To find the median, we identify the middle value of the ordered list, which, given that there are 9 numbers, is the fifth number: \( 6 \). So, with a mean of \( 9 \) and a median of \( 6 \), that reinforces the idea that in this dataset, the mean does indeed exceed the median, reflecting how skewed distributions can influence these two essential statistics. So, who knew numbers could tell such intriguing stories?
