Mean Median Mode Range Worksheets - Math Monks - Free Printable

To solve the problem, we need to analyze the bar graph and calculate the mean, median, mode, and range for the given data. Let's break it down step by step.

Step 1: Extract Data from the Bar Graph

From the bar graph, we can extract the following data:

- Tea:
- Emily: 25
- Ava: 15
- Andy: 20

- Coffee:
- Emily: 25
- Ava: 10
- Andy: 20

- Sandwich:
- Emily: 5
- Ava: 18
- Andy: 22

Step 2: Solve Each Part of the Problem

#### Part 1: Tea and Sandwich Eaten by Andy This Summer
Andy's data:
- Tea: 20
- Sandwich: 22

##### Mean:
\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{20 + 22}{2} = \frac{42}{2} = 21
\]

##### Median:
The values are already in order: 20, 22.
\[
\text{Median} = \frac{20 + 22}{2} = 21
\]

##### Mode:
There is no repeated value.
\[
\text{Mode} = \text{None}
\]

##### Range:
\[
\text{Range} = \text{Maximum value} - \text{Minimum value} = 22 - 20 = 2
\]

Answer for Part 1:
\[
\text{Mean: } 21, \text{ Median: } 21, \text{ Mode: } \text{None}, \text{ Range: } 2
\]

#### Part 2: Coffee and Sandwich Eaten by Emily This Summer
Emily's data:
- Coffee: 25
- Sandwich: 5

##### Mean:
\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{25 + 5}{2} = \frac{30}{2} = 15
\]

##### Median:
The values are already in order: 5, 25.
\[
\text{Median} = \frac{5 + 25}{2} = 15
\]

##### Mode:
There is no repeated value.
\[
\text{Mode} = \text{None}
\]

##### Range:
\[
\text{Range} = \text{Maximum value} - \text{Minimum value} = 25 - 5 = 20
\]

Answer for Part 2:
\[
\text{Mean: } 15, \text{ Median: } 15, \text{ Mode: } \text{None}, \text{ Range: } 20
\]

#### Part 3: Tea and Sandwich Eaten by Ava This Summer
Ava's data:
- Tea: 15
- Sandwich: 18

##### Mean:
\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{15 + 18}{2} = \frac{33}{2} = 16.5
\]

##### Median:
The values are already in order: 15, 18.
\[
\text{Median} = \frac{15 + 18}{2} = 16.5
\]

##### Mode:
There is no repeated value.
\[
\text{Mode} = \text{None}
\]

##### Range:
\[
\text{Range} = \text{Maximum value} - \text{Minimum value} = 18 - 15 = 3
\]

Answer for Part 3:
\[
\text{Mean: } 16.5, \text{ Median: } 16.5, \text{ Mode: } \text{None}, \text{ Range: } 3
\]

#### Part 4: Tea, Coffee, and Sandwich Eaten by All Three This Summer
Data for all three:
- Tea: 25 (Emily), 15 (Ava), 20 (Andy)
- Coffee: 25 (Emily), 10 (Ava), 20 (Andy)
- Sandwich: 5 (Emily), 18 (Ava), 22 (Andy)

Combine all values:
\[
25, 15, 20, 25, 10, 20, 5, 18, 22
\]

##### Mean:
\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{25 + 15 + 20 + 25 + 10 + 20 + 5 + 18 + 22}{9} = \frac{160}{9} \approx 17.78
\]

##### Median:
Arrange the values in ascending order:
\[
5, 10, 15, 18, 20, 20, 22, 25, 25
\]
The median is the middle value (5th value):
\[
\text{Median} = 20
\]

##### Mode:
The most frequent value(s):
\[
\text{Mode} = 20, 25
\]

##### Range:
\[
\text{Range} = \text{Maximum value} - \text{Minimum value} = 25 - 5 = 20
\]

Answer for Part 4:
\[
\text{Mean: } 17.78, \text{ Median: } 20, \text{ Mode: } 20, 25, \text{ Range: } 20
\]

Final Answers:

1. Tea and sandwich eaten by Andy:
\[
\boxed{21, 21, \text{None}, 2}
\]

2. Coffee and sandwich eaten by Emily:
\[
\boxed{15, 15, \text{None}, 20}
\]

3. Tea and sandwich eaten by Ava:
\[
\boxed{16.5, 16.5, \text{None}, 3}
\]

4. Tea, coffee, and sandwich eaten by all three:
\[
\boxed{17.78, 20, 20, 25, 20}
\]