Consider the following n = 11 observations on shear strength of a joint bonded in a particular manner (Exi = 514.90): 4.4 16.4 22.2 30.0 33.1 36.6 40.4 66.7 73.7 81.5 109.9 Determine the value of the 14% trimmed mean given the following (express your answer to 3 decimal places: x.XXx): Mean 46.809 9.09% trimmed mean (1/11) 44.511 18.18% trimmed mean (2/11) 43.243 Median 36 600
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Analysis of Shear Strength Data for Joint Bonding
The following data represents 11 observations on the shear strength of a joint bonded in a particular manner, with a sum of all observations (ΣXi) equal to 514.90:
**Observations:**
- 4.4
- 16.4
- 22.2
- 30.0
- 33.1
- 36.6
- 40.4
- 66.7
- 73.7
- 81.5
- 109.9
#### Statistical Measures:
The objective is to determine the value of the 14% trimmed mean, given the detailed statistical measures already provided:
- **Mean (µ):** The arithmetic average of the observations:
\[
\text{Mean} = 46.809
\]
- **9.09% Trimmed Mean (1/11):** The mean calculated after removing the lowest and highest 9.09% of data points:
\[
9.09\% \text{ trimmed mean} = 44.511
\]
- **18.18% Trimmed Mean (2/11):** The mean calculated after removing the lowest and highest 18.18% of data points:
\[
18.18\% \text{ trimmed mean} = 43.243
\]
- **Median:** The middle value of the data set when arranged in ascending order:
\[
\text{Median} = 36.600
\]
#### Calculating the 14% Trimmed Mean:
To calculate the 14% trimmed mean, 14% of the total number of observations (n = 11) needs to be calculated. Since 14% of 11 is approximately 1.54, we trim the data by removing the lowest and highest values, so approximately one value from each end can be trimmed.
Detailed steps:
1. **Sort the Data:**
\[
\{4.4, 16.4, 22.2, 30.0, 33.1, 36.6, 40.4, 66.7, 73.7, 81.5, 109.9\}
\]
2. **Remove the Lowest and Highest Approximate 1.54 Values:**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F885800f4-ea55-4813-8161-e1df31cc31af%2F36f22ca6-076f-429e-b8b1-f9754af7e113%2F7wlzmbr_processed.jpeg&w=3840&q=75)
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