QQuestionMathematics
QuestionMathematics
What is the median of this data set?
# Shield Darter
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Answer
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Step 1:: Extract the data from the given image and organize it into a list.
The given data set is as follows: 12, 13, 15, 15, 16, 16, 16, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 32, 32, 33, 34, 34, 35, 35, 36, 36, 37, 38, 39, 40, 41, 42, 43, 44
Step 2:: Determine the number of data points in the set.
There are 50 data points in the set.
Step 3:: Find the median based on the number of data points.
Since there are 50 data points, the median is the average of the $\frac{50+1}{2} = 25.5$th and 25.6th data points.
Step 4:: Identify the 25.5th and 25.6th data points.
To find the 25.5th and 25.6th data points, we need to interpolate between the values around these positions. The 25th data point is 24, the 26th data point is 25, and the 27th data point is 26.
Step 5:: Calculate the average of the 25.5th and 25.6th data points.
The 25.6th data point is halfway between 25 and 26, so it is $\frac{25 + 26}{2} = 25.5$.
Step 6:: Compute the median.
The median is the average of the 25.5th and 25.6th data points, which is $\frac{24.5 + 25.5}{2} = 25$.
Final Answer
The median of the data set is 25.
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