Question

Use the given sample data to find Q3 49 52 52 52 74 67 55 55

Answer 1

The third quartile (Q3) of the given sample data is 67, indicating that 75% of the data is at or below this value.

Step-by-step explanation:

To find the third quartile (Q3) of the given sample data, we first need to organize the data in ascending order. The provided numbers are already sorted: 49, 52, 52, 52, 55, 55, 67, 74. The third quartile Q3, also known as the 75th percentile, is the value below which 75% of the data falls. Since we have 8 data points, we take the following approach:

1. Calculate the position of Q3: (0.75) * (n+1) = 0.75 * (8+1) = 6.75.
2. Since the position is not a whole number, we round up to the next whole number, which is 7. This means Q3 is the 7th data point in the ordered set.
3. Locate the 7th value in the ordered set, which is 67.

Therefore, the third quartile (Q3) for the data set is 67, indicating that 75% of the scores are equal to or less than this value.