Question
Using the list of numbers below, which statement is true? \( \begin{array}{rllllllll}5 & 5 & 5 & 8 & 10 & 13 & 19 & 20 & 20 \\ 29 & 34 & 36 & & & & & & \end{array} \)
Ask by Hodgson Lawson. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The mode is 5, the median is 16, and the mean is 17.
Solution
1. **List the Numbers in Order:**
The numbers given are
\[
5,\; 5,\; 5,\; 8,\; 10,\; 13,\; 19,\; 20,\; 20,\; 29,\; 34,\; 36.
\]
2. **Determine the Mode:**
The mode is the number that appears most often.
- \(5\) appears three times
- \(20\) appears twice
Thus, the mode is
\[
5.
\]
3. **Determine the Median:**
With \(12\) numbers, the median is the average of the 6th and 7th numbers.
- 6th number: \(13\)
- 7th number: \(19\)
So, the median is
\[
\frac{13 + 19}{2} = 16.
\]
4. **Determine the Mean:**
First, find the sum of the numbers:
\[
5 + 5 + 5 + 8 + 10 + 13 + 19 + 20 + 20 + 29 + 34 + 36 = 204.
\]
Since there are \(12\) numbers, the mean is
\[
\frac{204}{12} = 17.
\]
5. **Compare the Values:**
We have:
- Mode: \(5\)
- Median: \(16\)
- Mean: \(17\)
This shows that the mode is considerably less than the median and the mean, and the mean is slightly greater than the median.
Therefore, the true statement is:
\[
\text{In this list, the mode is } 5,\; \text{the median is } 16,\; \text{and the mean is } 17.
\]
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Extra Insights
The list of numbers you provided seems to show a collection of integers. A true statement regarding this list is that the median is the average of the two middle numbers when sorted. In this case, the total number of observations is 13, with the middle number being the 7th value in the ordered list, which is 19. Another true statement is that the mode of this dataset is 5 and 20 since both numbers appear three times, more than any other number. This indicates that when it comes to the most frequently occurring values in the list, both 5 and 20 have the spotlight!