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 x 10 psi): 5.7 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 11.5 11.8 10.6 (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.) Stems Leaves 7. 00234677889 8. 127 9 077 10 11 What appears to be a representative strength value? v MPa 7.7 Do the observations appear to be highly concentrated about the representative value or rather spread out? O highly concentrated around the representative value O spread out with a large range
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 x 10 psi):
5.7
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
11.5
11.8
10.6
(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.)
Stems
Leaves
7.
00234677889
8
127
077
10
11
What appears to be a representative strength value?
7.7
MPa
Do the observations appear to be highly concentrated about the representative value or rather spread out?
O highly concentrated around the representative value
O 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?
reasonably symmetric
O positive skewness
O negative skewness
O completely random distribution
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