i need help with my homework.
Using the following set of data, calculate the lower quartile, the upper quartile, and the interquartile range.
20, 22, 25, 28, 29, 30, 32, 33, 34
Be sure to show your work for finding:
the lower quartile
the upper quartile
the interquartile range
To find the lower quartile, upper quartile, and interquartile range, you need to follow these steps:
Step 1: Arrange the data in ascending order: 20, 22, 25, 28, 29, 30, 32, 33, 34.
Step 2: Calculate the position of the lower quartile (Q1) using the formula (n + 1) / 4, where n is the number of data points in the set. In this case, there are 9 data points, so (9 + 1) / 4 = 10 / 4 = 2.5. Since 2.5 is not a whole number, we need to find the average of the two middle values. The second and third values are 22 and 25, so the lower quartile is (22 + 25) / 2 = 23.5.
Step 3: Calculate the position of the upper quartile (Q3) using the formula (3 * (n + 1)) / 4. Applying the formula, (3 * (9 + 1)) / 4 = 30 / 4 = 7.5. Since 7.5 is not a whole number, we need to find the average of the two middle values. The seventh and eighth values are 32 and 33, so the upper quartile is (32 + 33) / 2 = 32.5.
Step 4: Calculate the interquartile range (IQR) by subtracting the lower quartile (Q1) from the upper quartile (Q3). In this case, 32.5 - 23.5 = 9.
Therefore, the lower quartile is 23.5, the upper quartile is 32.5, and the interquartile range is 9.
see your previous post
repeat posts just waste time.