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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): 5.7 7.2 7.3 6.1 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 11.4 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 5 6 7 8 9 10 11 What appears to be a representative strength value? MPa Do the observations appear to be highly concentrated about the representative value or rather spread out? 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? 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? (Round your answer to two decimal places.)

Explanation / Answer

a) Stem and Leaf Display of the data-

The decimal point is at the |

5 | 7
6 | 13588
7 | 00234677889
8 | 127
9 | 077
10 | 6
11 | 468

7 Appears to be a representative stregth value.

Yes the observations are more or less highly concentrated abou the representative value

b) THe distribution is not symmetric. It is more likely to be a positively skewed.

c)If we do boxplot we can see 11.8 is showed as an outlier.

d)4 observations out of 27 are exceeding 10 Mpa.

So the proportion of stregth obs in sample exceeding 10 Mpa is 14.8%

The R code is attached Below

x=c( 5.7, 7.2, 7.3, 6.1, 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, 11.4 ,11.8 ,10.6)
stem(x)
boxplot(x)
which(x>10)

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