To analyze the relationship between the mean and median based on the data represented in the graph, we first need to translate the visual information into numerical values.
The graph indicates the following data points:
- 5 occurrences of the value 1,
- 4 occurrences of the value 2,
- 3 occurrences of the value 3,
- 2 occurrences of the value 4,
- 1 occurrence of the value 5.
Now, let's list out all the values in the dataset:
- Value 1 appears 5 times: 1, 1, 1, 1, 1
- Value 2 appears 4 times: 2, 2, 2, 2
- Value 3 appears 3 times: 3, 3, 3
- Value 4 appears 2 times: 4, 4
- Value 5 appears 1 time: 5
Combining all of this, we have the dataset: 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5
Calculate the Mean:
- Total count of values = 5 + 4 + 3 + 2 + 1 = 15
- Sum of the values = (51) + (42) + (33) + (24) + (1*5) = 5 + 8 + 9 + 8 + 5 = 35
- Mean = Total Sum / Total Count = 35 / 15 = 2.33 (approx)
Calculate the Median:
To find the median, we look at the sorted list. The median is the value in the middle position of a sorted dataset:
- Since there are 15 data points (odd number), the median will be the 8th value.
- The ordered dataset is: 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5.
- The 8th value is 2.
Compare Mean and Median:
Now we can compare the mean and median values:
- Mean = 2.33 (approx)
- Median = 2
Since 2.33 is greater than 2, the correct answer is:
Option #1: The mean is greater than the median.