To find the median, lower quartile, and upper quartile of the given set of data (8, 3, 5, 5, 4, 7), follow these steps:
Step 1: Arrange the data in ascending order: 3, 4, 5, 5, 7, 8.
Step 2: Find the median:
Since there are six data points, the median is the average of the two middle values. The middle values are 5 and 5, so the median is (5 + 5) / 2 = 5.
Step 3: Find the lower quartile (Q1) and upper quartile (Q3):
To find the quartiles, divide the data set into four equal parts.
Lower quartile (Q1): Since there are six data points, Q1 is the median of the lower half of the data set. The lower half is 3, 4, and 5. The median of this lower half is (3 + 4) / 2 = 3.5.
Upper quartile (Q3): Similarly, Q3 is the median of the upper half of the data set. The upper half is 5, 7, and 8. The median of this upper half is (7 + 8) / 2 = 7.5.
The calculations for the median, lower quartile, and upper quartile are as follows:
Median: 5
Lower quartile (Q1): 3.5
Upper quartile (Q3): 7.5
To construct a box-and-whisker plot, you can represent the data points on a number line and plot the minimum value (3), Q1 (3.5), median (5), Q3 (7.5), and maximum value (8) as a box-and-whisker plot. The line segment within the box represents the interquartile range, while the distance between the minimum and maximum values represents the range.
Using the box-and-whisker plot, you can find the range and interquartile range:
Range: The range is the difference between the maximum and minimum values. In this case, the range is 8 - 3 = 5.
Interquartile range (IQR): The IQR is the difference between Q3 and Q1. In this case, the IQR is 7.5 - 3.5 = 4.
Make sure to draw your own box-and-whisker plot on paper to visually represent the data.