Question 35·Medium·One-Variable Data Distributions; Measures of Center and Spread
The number of goals scored by a soccer team in each of nine consecutive matches is as follows:
0, 2, 1, 3, 2, 1, 4, 2, 1
What is the median number of goals scored in these nine matches?
For median questions, always start by writing the data in numerical order. Then quickly count how many values there are: if the count is odd, go directly to the single middle position; if it is even, identify the two middle positions and average those two values. Avoid mixing up median with mean (average) or mode (most frequent value), and use simple counting to stay accurate and fast.
Hints
Remember what the median is
The median is the middle value of a data set when the numbers are in order from smallest to largest. Start by rewriting the list in order.
Use the fact that there are 9 matches
Count how many goal counts there are. Since the number of values is odd, you will not need to average two numbers; there is one single middle value.
Find the middle position
For 9 ordered numbers, which position in the list is exactly in the middle? Once you know that position, count to that place in your ordered list.
Desmos Guide
Use Desmos to compute the median
In an expression line, type:
median([0,2,1,3,2,1,4,2,1])
Desmos will output a single number; that value is the median of the nine matches.
Step-by-step Explanation
Put the data in order
The original list of goals is: 0, 2, 1, 3, 2, 1, 4, 2, 1.
To find the median, first sort the numbers from smallest to largest:
0, 1, 1, 1, 2, 2, 2, 3, 4.
Identify the position of the median
Count how many data values there are.
There are matches, so there are numbers in the list.
When there is an odd number of data values, the median is the value in the exact middle position of the ordered list.
The middle position for values is the th value (because 4 values will be on each side of it).
Find the value at the middle position
From the ordered list
0, 1, 1, 1, 2, 2, 2, 3, 4
count to the 5th number:
- 1st: 0
- 2nd: 1
- 3rd: 1
- 4th: 1
- 5th: 2
The 5th value is 2, so the median number of goals scored in these nine matches is 2.