Find the median and mean of the data set below: 31, 38, 35, 36, 3
Check the final answer first, then review the worked steps.
Problem
Find the median and mean of the data set below: 31, 38, 35, 36, 3
Answer
\(Median = 35, Mean = 28.6\)
Step-by-step solution
- Order the data set: To find the median, we must first arrange the numbers in ascending order. The given data set is $31, 38, 35, 36, 3$. Ordering these from least to greatest gives: $3, 31, 35, 36, 38$.
- Find the median: The median is the middle value of an ordered data set. Since there are $n = 5$ numbers (an odd number), the median is the value at the position $\frac{n+1}{2} = \frac{5+1}{2} = 3$rd position. Looking at our ordered list $3, 31, 35, 36, 38$, the $3$rd value is $35$.
- Find the mean: The mean is the sum of all values divided by the total number of values. First, calculate the sum: $3 + 31 + 35 + 36 + 38 = 143$. Then, divide by the total count, which is $5$: $\text{Mean} = \frac{143}{5} = 28.6$.