Flexural strength is a measure of a material's ability to resist failure in bending. The accompanying data are on flexural strength of concrete (in MegaPascal, MPa, where 1 Pa (Pascal) = 1.45 ⨯ 10−4 psi): 5.6 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0 8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.2 11.8 10.5 (a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) Answer: Stems Leaves 5 6 7 8 9 10 11 What appears to be a representative strength value? Answer:____________ MPa Do the observations appear to be highly concentrated about the representative value or rather spread out? Answer: ______highly concentrated around the representative value ______spread out with a large range (b) Does the display appear to be reasonably symmetric about a representative value, or would you describe its shape in some other way? Answer: _____reasonably symmetric ____positive skewness ____negative skewness ____completely random distribution (c) Do there appear to be any outlying strength values? Yes or No (d) What proportion of strength observations in this sample exceed 10 MPa? (Round your answer to two decimal places.) Answer:____________
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.
Flexural strength is a measure of a material's ability to resist failure in bending. The accompanying data are on flexural strength of concrete (in MegaPascal, MPa, where 1 Pa (Pascal) = 1.45 ⨯ 10−4 psi):
| 5.6 | 7.2 | 7.3 | 6.3 | 8.1 | 6.8 | 7.0 | 7.6 | 6.8 | 6.5 | 7.0 | 6.3 | 7.9 | 9.0 |
| 8.2 | 8.7 | 7.8 | 9.7 | 7.4 | 7.7 | 9.7 | 7.8 | 7.7 | 11.6 | 11.2 | 11.8 | 10.5 |
| Stems | Leaves |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | |
| 10 | |
| 11 |
What appears to be a representative strength value?
Answer:____________ MPa
Do the observations appear to be highly concentrated about the representative value or rather spread out?
(b) Does the display appear to be reasonably symmetric about a representative value, or would you describe its shape in some other way?
(c) Do there appear to be any outlying strength values?
(d) What proportion of strength observations in this sample exceed 10 MPa? (Round your answer to two decimal places.)
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