Answer :
The largest value among the mean, median, and mode is the mean, which is approximately 87.67.
To determine which is the largest (mean, median, or mode) for the given data set, we must calculate each of these statistical measures.
Data set: 80, 83, 83, 83, 87, 87, 91, 97, 98
1. **Mean (Average):**
To calculate the mean, we add up all the numbers and then divide by the count of numbers.
Mean = (80 + 83 + 83 + 83 + 87 + 87 + 91 + 97 + 98) / 9
Mean = 789 / 9
Mean = 87.666... (Repeating)
2. **Median (Middle Value):**
To find the median, we need to order the data set from smallest to largest and find the middle value. For an odd number of observations, the median is the middle number.
The data set is already ordered, and there are 9 numbers. The middle one is the 5th number (since there are 4 numbers on each side of it).
Median = 87 (which is the 5th number in the ordered set)
3. **Mode (Most Frequent Value):**
The mode is the number that appears most frequently.
In the given data set, the number 83 appears three times, which is more than any other number.
Mode = 83
Finally, we compare the mean, median, and mode to identify which is the largest.
Mean ≈ 87.67, Median = 87, Mode = 83
Therefore the largest value among the mean, median, and mode is the mean, which is approximately 87.67.
