Flexural strength is a measure of a material\'s ability to resist failure in ben

Question

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 times 10^-4 psi): 5.6 7.2 7.3 6.2 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 10.5 (a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter the word NONE for sterns with no values.) What appears to be the median strength value? MPa Do the observations appear to be highly concentrated about the median or rather spread nut? highly concentrated around the representative value spread out with a large range (b) Does the display appear to be reasonably symmetric about the median, or would you describe its shape in some other way? reasonably symmetric positive skewness negative skewness completely random distribution (c) Do there appear to be any outlying strength values? Yes NO (d) What proportion of strength observations in this sample exceed 10 MPa?

Explanation / Answer

(a)

Followig is the stem and leaf display of the data:

Since there are 27 data values so median will be 14th data value. So median is 7.7 MPa.

Highly concentrated about the representative value.

(b)

Stem and leaf display shows that the data is positively skewed.

(c)

No

(d)

Out of 27 data values, 4 data vaues exceed 10 MPa so required proprotion is

4 / 27 = 0.15

Stem and Leaf plot for X stem unit = 1 leaf unit = 0.1 Frequency Stem Leaf 1 5 6 5 6 2 3 5 8 8 11 7 0 0 2 3 4 6 7 7 8 8 9 3 8 1 2 7 3 9 0 7 7 1 10 5 3 11 5 6 8 27

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