The values from a stem-and-leaf plot are:27,27,29,33,38,44,44,44,46,50,58,in numerical order.Please explain how to find the lower quartile for this set.
I would take the median of the first five values 27,27,29,33,38;this would make 29 the lower quartile.Is this correct? Is this properly worded?
Thank You.
To find the lower quartile for a given set of data, you need to follow these steps:
1. Arrange the data in numerical order.
In this case, the given data is already in numerical order: 27, 27, 29, 33, 38, 44, 44, 44, 46, 50, 58.
2. Determine the position of the lower quartile.
The lower quartile represents the 25th percentile, which means that 25% of the data falls below it. To find the position, use the formula:
Position = (25 / 100) * (n + 1)
In this case, n = 11 (the number of data points), so the position = (25 / 100) * (11 + 1) = 3.
3. Find the value at the determined position.
Since the position is not a whole number (3), you need to take the average of the two values that surround it. In this case, the values at position 3 are 27 and 29.
Therefore, the lower quartile (Q1) for this set is 28 (the average of 27 and 29).
Regarding your question about using the median of the first five values, it is not the correct method for finding the lower quartile. The lower quartile is not the median of only a subset of the data; it represents the 25th percentile of the entire dataset.
As for your wording, you should say, "To find the lower quartile for this set, arrange the data in numerical order. Then, determine the position of the lower quartile by calculating (25 / 100) * (n + 1), where n is the number of data points. Finally, find the value at the determined position."