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# Median

## Middle number of ascending values.

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Median

Have you ever tried to figure out the middle number of a set of data?

Tania has her carrot counts organized. Now she wants to figure out the middle number of carrots that were picked. Here is Tania’s data about the number of carrots picked each week over nine weeks of harvest.

2, 8, 8, 14, 9, 12, 14, 20, 19, 14

This is a total of 120 carrots-the number of carrots that we saw from the last Concept.

In this Concept, you will learn how to help Tania figure out the median number of carrots picked during the harvest season.

### Guidance

The median of a set of data is the middle score of the data. Medians are useful whenever we are trying to figure out what the middle of a set of data is. For example, let’s say that we are working to figure out what a median amount of money is or for a runner what a median time is.

2, 5, 6, 2, 8, 11, 13, 14, 15, 21, 22, 25, 27

Here is a set of data. To find the median of a set of data we need to do a couple of things.

1. Write the numbers in order from the smallest to the greatest. Be sure to include repeated numbers in the list.

If we do that with this set, here are our results.

2, 2, 5, 6, 8, 11, 13, 14, 15, 21, 22, 25, 27

2. Next, we find the middle number of the set of data.

In this set, we have an odd number of values in the set. There are thirteen numbers in the set. We can count 6 on one side of the median and six on the other side of the median.

This set of data was easy to work with because there was an odd number of values in the set. What happens when there is an even number of values in the set?

4, 5, 12, 14, 16, 18

Here we have six values in the data set. They are already written in order from smallest to greatest so we don’t need to rewrite them. Here we have two values in the middle because there are six values.

4, 5, 12, 14, 16, 18

The two middle values are 12 and 14. We need to find the middle value of these two values. To do this, we take the average of the two scores.

The median score is 13.

Now let's practice. Find the median of each set of data.

5, 6, 8, 11, 15

Solution: 8

#### Example B

4, 1, 6, 9, 2, 11

Solution: 5

#### Example C

23, 78, 34, 56, 89

Solution: 56

Now back to the original problem. Here is Tania’s data about the number of carrots picked each week over nine weeks of harvest.

2, 8, 8, 14, 9, 12, 14, 20, 19, 14

What is the middle number of carrots that were picked?

This question is asking us to find the median or middle number. We look at a set of data listed in order.

2, 8, 8, 9, 12, 14, 14, 14, 19, 20

The median is between 12 and 14.

The median number is 13.

### Vocabulary

Maximum
the greatest score in a data set
Minimum
the smallest score in a data set
Median
the middle score in a data set

### Guided Practice

Here is one for you to try on your own.

Jess has planted a garden. His big crop has been eggplant. Jess harvested the following numbers of eggplant over five days.

12, 9, 15, 6, 9

What is the median number of eggplant harvested?

To figure this out, we must first write the numbers in order from least to greatest.

6, 9, 9, 12, 15

Notice that 9 is included twice.

Then we find the middle score.

The median number of eggplant harvested was 9 eggplant.

### Practice

Directions: Find the median for each pair of numbers.

1. 16 and 19

2. 4 and 5

3. 22 and 29

4. 27 and 32

5. 18 and 24

Directions: Find the median for each set of numbers.

6. 4, 5, 4, 5, 3, 3

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

### Vocabulary Language: English

cumulative frequency

cumulative frequency

Cumulative frequency is used to determine the number of observations that lie above (or below) a particular value in a data set.
Maximum

Maximum

The largest number in a data set.
Median

Median

The median of a data set is the middle value of an organized data set.
Minimum

Minimum

The minimum is the smallest value in a data set.
normal distributed

normal distributed

If data is normally distributed, the data set creates a symmetric histogram that looks like a bell.
outliers

outliers

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.