To calculate the mean, median, and spread for the dataset represented in the bar graph, we first need to extract the data points based on the information provided:
- At x = 10, the height is 2 → Dataset: 10, 10
- At x = 11, the height is 4 → Dataset: 11, 11, 11, 11
- At x = 12, the height is 4 → Dataset: 12, 12, 12, 12
- At x = 13, the height is 2 → Dataset: 13, 13
Combining these, the complete dataset is: \[ [10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13] \]
1. Mean:
To find the mean, we sum all values and divide by the number of values.
Sum = \( 10 + 10 + 11 + 11 + 11 + 11 + 12 + 12 + 12 + 12 + 13 + 13 = 102 + 114 + 124 + 132 = 20 + 44 + 48 + 26 = 138 \)
Number of values = 12
Mean = \( \frac{138}{12} = 11.5 \)
2. Median:
To find the median, we need to arrange the dataset in ascending order (which it already is):
\[ [10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13] \]
Since there are 12 values (even number), the median is the average of the 6th and 7th values.
6th value = 11 7th value = 12
Median = \( \frac{11 + 12}{2} = \frac{23}{2} = 11.5 \)
3. Spread:
The spread can be calculated as the range of the data, which is the difference between the maximum and minimum values.
Minimum value = 10 Maximum value = 13
Spread = Maximum - Minimum = \( 13 - 10 = 3 \)
Summary of Results:
- The mean = 11.5
- The median = 11.5
- The spread = 3
Thus, we have:
- Mean = 11.5
- Median = 11.5
- Spread = 3