Thank you for visiting Consider the following observations on shear strength of a joint bonded in a particular manner 30 0 4 4 33 1 66 7 81 5. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
The sample mean is 49.82, the sample median is 36.75. The mean and median are different because of extreme values. The lower quartile (LQ) is 10.4 and the upper quartile (UQ) is 77.6. The trimmed mean is 45.26 with a trimming percentage of 18.18%.
Explanation:
a. To find the sample mean, we sum up all the observations and divide by the total number of observations. In this case, the sample mean is (30.0 + 4.4 + 33.1 + 66.7 + 81.5 + 22.2 + 40.4 + 16.4 + 73.7 + 36.6 + 109.9) / 11 = 49.82.
b. To find the sample median, we arrange the observations in ascending order and find the middle value. In this case, the median is the average of the two middle values: (33.1 + 40.4) / 2 = 36.75.
c. The mean and median are different because the presence of extreme values, such as 109.9 and 4.4, can pull the mean away from the central tendency. This is especially true in this case where the extreme values are much larger or smaller than the other observations.
d. To find the lower quartile (LQ), we arrange the observations in ascending order and find the middle value of the lower half. Since there are 11 observations, the LQ is the 11th value divided by 4: 11/4 = 2.75. So the LQ is the average of the 2nd and 3rd observations: (4.4 + 16.4) / 2 = 10.4.
e. To find the upper quartile (UQ), we arrange the observations in ascending order and find the middle value of the upper half. Since there are 11 observations, the UQ is the 3 * (11/4) = 8.25 value. So the UQ is the average of the 8th and 9th observation: (73.7 + 81.5) / 2 = 77.6.
f. To calculate a trimmed mean by deleting the smallest and largest observations, we remove the 4.4 and 109.9 values. Then we find the mean of the remaining values: (30.0 + 33.1 + 66.7 + 81.5 + 22.2 + 40.4 + 16.4 + 73.7 + 36.6) / 9 = 45.26. The corresponding trimming percentage is 2/11 * 100% = 18.18%.
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