To analyze the dataset represented in the bar graph, we need to first extract the actual values and their frequencies.
From the graph data:
- 5 appears 6 times
- 6 appears 5 times
- 7 appears 4 times
- 8 appears 3 times
Now, we can list the dataset based on these frequencies:
- Six 5s: 5, 5, 5, 5, 5, 5
- Five 6s: 6, 6, 6, 6, 6
- Four 7s: 7, 7, 7, 7
- Three 8s: 8, 8, 8
Putting all those values together, we get the following dataset:
\[ 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8 \]
Step 1: Calculate the Mean
To calculate the mean, sum all values and divide by the total number of values.
\[ \text{Mean} = \frac{(5 \times 6) + (6 \times 5) + (7 \times 4) + (8 \times 3)}{6 + 5 + 4 + 3} \]
Calculating the sum:
\[ = \frac{(30) + (30) + (28) + (24)}{18} = \frac{112}{18} \approx 6.22 \]
Step 2: Calculate the Median
To find the median, we first need to arrange the dataset in ascending order (already arranged) and identify the middle value.
Since we have 18 numbers (even count), the median will be the average of the 9th and 10th values.
From the dataset:
- 1st to 6th: 5
- 7th to 11th: 6
- 12th to 15th: 7
- 16th to 18th: 8
The 9th and 10th values are both 6.
\[ \text{Median} = \frac{6 + 6}{2} = 6 \]
Step 3: Calculate the Spread (Range)
The range is defined as the difference between the maximum and minimum values in the dataset.
\[ \text{Range} = \text{Maximum} - \text{Minimum} = 8 - 5 = 3 \]
Summary of Results
- Mean: Approximately 6.22
- Median: 6
- Range: 3