Explore your Data: Mode, median and mean - MAKE ME ANALYST - Free Printable

Let's solve the Measures of Central Tendency worksheet step by step, filling in the blanks and solving the examples.

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✔ Part 1: Fill in the Blanks

#### MEAN
- Definition: The average of a set of numbers
- How to find it: Add all the numbers then divide by how many numbers there are
- How many: A set of numbers will only have one mean

#### MEDIAN
- Definition: The middle number in a set of ordered numbers
- How to find it: Order the numbers from least to greatest, then find the number(s) in the middle
- How many: A set of numbers will only have one median. If two numbers are in the middle, find the mean (average) of those two numbers

#### MODE
- Definition: The number that occurs most frequently in a set of numbers
- How to find it: Order the numbers from least to greatest, then find the number(s) that occur the most often
- How many: A set of numbers could have no, one, or more than one modes

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✔ Example 1:

Data Set: 1, 5, 10, 16, 8, 9, 3, 5, 7, 11

#### Step 1: Order the numbers
Arrange from least to greatest:
1, 3, 5, 5, 7, 8, 9, 10, 11, 16

#### Step 2: Find the Mean
- Add all numbers:
$1 + 3 + 5 + 5 + 7 + 8 + 9 + 10 + 11 + 16 = 75$
- Divide by number of values (10):
$ \frac{75}{10} = 7.5 $

✔ Mean = 7.5

#### Step 3: Find the Median
- There are 10 numbers (even), so the median is the average of the 5th and 6th numbers.
- 5th number = 7, 6th number = 8
- $ \frac{7 + 8}{2} = 7.5 $

✔ Median = 7.5

#### Step 4: Find the Mode
- Look for the number that appears most frequently.
- 5 appears twice; all others appear once.
- So, 5 is the mode.

✔ Mode = 5

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✔ Example 2:

Test Scores: 72, 75, 66, 98, 83, 84, 72, 53, 88, 100, 75, 78

#### Step 1: Order the numbers
53, 66, 72, 72, 75, 75, 78, 83, 84, 88, 98, 100

(There are 12 numbers)

#### Step 2: Find the Mean
- Add all numbers:
$53 + 66 + 72 + 72 + 75 + 75 + 78 + 83 + 84 + 88 + 98 + 100 = 924$
- Divide by 12:
$ \frac{924}{12} = 77 $

✔ Mean = 77

#### Step 3: Find the Median
- Even number of values (12), so median is average of 6th and 7th numbers.
- 6th = 75, 7th = 78
- $ \frac{75 + 78}{2} = 76.5 $

✔ Median = 76.5

#### Step 4: Find the Mode
- Count frequency:
- 72 → 2 times
- 75 → 2 times
- All others → 1 time
- Two numbers (72 and 75) appear most frequently (twice each)
- So, this data set has two modes: 72 and 75

✔ Mode = 72 and 75 (bimodal)

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✔ Final Answers:

#### Example 1:
- Mean: 7.5
- Median: 7.5
- Mode: 5

#### Example 2:
- Mean: 77
- Median: 76.5
- Mode: 72 and 75

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📝 Summary Table (Completed):

| WORD | DEFINITION | HOW TO FIND IT | HOW MANY |
|--------|--------------------------------------------|----------------------------------------------------------------------------------|------------------------------------------------|
| MEAN | The average of a set of numbers | Add all the numbers then divide by how many numbers there are | A set of numbers will only have one mean |
| MEDIAN | The middle number in a set of ordered numbers | Order the numbers from least to greatest, then find the number(s) in the middle | A set of numbers will only have one median. If two numbers are in the middle, find the mean |
| MODE | The number that occurs most frequently in a set of numbers | Order the numbers from least to greatest, then find the number(s) that occur the most often | A set of numbers could have no, one, or more than one modes |

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