11.2: Median
Have you ever wondered how fast a sled dog can travel?
Alaskan sled dogs travel varying speeds during the Iditarod. These strong, wonderful animals can travel at an average speed of anywhere from 5 to 15 miles per hours.
Here are some speeds from the last Iditarod.
10 mph
12 mph
8 mph
15 mph
9 mph
8 mph
7 mph
12 mph
Given these speeds, what was the median speed on the journey?
To answer this question, you will need to know how to identify and calculate a median. Pay attention and you will learn how to do this in this Concept.
Guidance
Now that you have learned about the mean of a set of data, let’s move on to the median. If you think about the word “median” you can think about the median in a road or street. The median of a street is in the middle of the street. Just like the median of a road, the median of a set of data is the middle value of the set of numbers.
The median is the middle number when the values are arranged in order from the least to the greatest.
Notice that a key to finding the median is that the values must be arranged in order from least to greatest. If they are not arranged in this way, you will not be able to determine an accurate median score!!!
Here is one to work on.
Find the median for the set of data: 47, 56, 51, 45, and 41.
Step 1: Arrange the data values in order from least to greatest.
41, 45, 47, 51, 56
Step 2: Determine the number in the middle of the data set. 47 is the median because it is the data value in the middle of the data set.
The median of the data set is 47.
Median scores are used when analyzing temperature. Take a look.
The chart below depicts the daily temperature in San Diego for the first seven days in August. Determine the median temperature.
Date: | Temperature: |
---|---|
Sunday 8/1 | \begin{align*}88^\circ F\end{align*} |
Monday 8/2 | \begin{align*}83^\circ F\end{align*} |
Tuesday 8/3 | \begin{align*}87^\circ F\end{align*} |
Wednesday 8/4 | \begin{align*}89^\circ F\end{align*} |
Thursday 8/5 | \begin{align*}82^\circ F\end{align*} |
Friday 8/6 | \begin{align*}79^\circ F\end{align*} |
Saturday 8/7 | \begin{align*}87^\circ F\end{align*} |
Step 1: Arrange the temperatures in order from least to greatest.
79, 82, 83, 87, 87, 88, 89
Step 2: Determine the data value in the middle of the data set. In this case, 87 is the median temperature.
The answer is \begin{align*}87^\circ F\end{align*}.
Here is a situation about test scores.
Katie’s first four test scores are 75%, 81%, 80%, and 84%. Determine the median of Katie’s test scores.
Step 1: Arrange the test scores in order from least to greatest.
75, 80, 81, 84
Step 2: In this case, there are two data values in the middle of the data set. To find the median, find the average of the two data values. Recall that to find the mean, determine the sum of the numbers and then divide by two.
\begin{align*}80 + 81 &= 161\\ 161 \div 2 &= 80.5\end{align*}
The median of Katie’s test scores is 80.5%.
Sometimes, you will have median scores that are not whole numbers. When this happens, be sure to include the decimal in your answer. This means that the median score is between two whole numbers.
Take a few minutes and write the steps to figuring out the median score down in your notebook.
Find the median score for each data set.
Example A
\begin{align*}12, 14, 15, 16, 18, 20\end{align*}
Solution: 15.5
Example B
\begin{align*}14, 18, 19, 34, 32, 30, 41, 50\end{align*}
Solution: 31
Example C
\begin{align*}5, 10, 23, 20, 7, 9, 11, 18, 35, 16, 22\end{align*}
Solution: 16
Here is the original problem once again.
Alaskan sled dogs travel varying speeds during the Iditarod. These strong, wonderful animals can travel at an average speed of anywhere from 5 to 15 miles per hours.
Here are some speeds from the last Iditarod.
10 mph
12 mph
8 mph
15 mph
9 mph
8 mph
7 mph
12 mph
Given these speeds, what was the median speed on the journey?
First, let's write these speeds in order from least to greatest.
7, 8, 8, 9, 10, 12, 12, 15
Now we can find the middle speed. Because there is an even number of speeds, we are looking for a value between 9 and 10.
The median speed is 9.5 mph.
Vocabulary
Here are the vocabulary words in this Concept.
- Data
- pieces of numerical information collected in a set.
- Mean
- the average value of a set of data.
- Median
- the middle value or score of set of data.
Guided Practice
Here is one for you to try on your own.
Find the median.
12, 14, 16, 11, 19, 12, 15, 16, 17, 22, 21
Answer
First, let's write these values in order from least to greatest.
11, 12, 12, 14, 15, 16, 16, 17, 19, 21, 22
The median value is 16.
Video Review
Here is a video for review.
- This is a Khan Academy video on mean, median and mode.
Practice
Directions: Find the median for each set of numbers.
1. 2, 1, 3, 4, 2, 1, 5, 6, 7, 2, 3
2. 11, 12, 17, 18, 21, 12, 13, 13
3. 20, 22, 21, 24, 25, 20, 19
4. 18, 17, 19, 21, 22, 20, 18, 17
5. 19, 29, 39, 49, 59, 69, 79, 89
6. 4, 5, 4, 5, 3, 3, 2, 3, 3, 2
7. 6, 7, 8, 3, 2, 4
8. 11, 10, 9, 13, 14, 16
9. 21, 23, 25, 22, 22, 27
10. 27, 29, 29, 32, 30, 32, 31
11. 34, 35, 34, 37, 38, 39, 39
12. 43, 44, 43, 46, 39, 50
13. 122, 100, 134, 156, 144, 110
14. 224, 222, 220, 222, 224, 224
15. 540, 542, 544, 550, 548, 547
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cumulative frequency
Cumulative frequency is used to determine the number of observations that lie above (or below) a particular value in a data set.Data
Data is information that has been collected to represent real life situations, usually in number form.Mean
The mean of a data set is the average of the data set. The mean is found by calculating the sum of the values in the data set and then dividing by the number of values in the data set.Median
The median of a data set is the middle value of an organized data set.normal distributed
If data is normally distributed, the data set creates a symmetric histogram that looks like a bell.outliers
An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.Image Attributions
Here you'll learn to find the median of a set of data.