Consider the strength data for beams given below :5.7 7.2 7.3 6.2 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.08.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.5 11.8 10.6Required:a. Construct a stem-and-leaf display of the data. What appears to be a representative strength value? 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?

(a) Shown below

(b) Positively Skewed

(c) No Outlier

(d) 15%

Step-by-step explanation:

Arrange the data set in ascending order as follows:

S = {5.7 , 6.2 , 6.3 , 6.5 , 6.8 , 6.8 , 7 .0, 7 .0, 7.2 , 7.3 , 7.4 , 7.6 , 7.7 , 7.7 , 7.8 , 7.8 , 7.9 , 8.1 , 8.2 , 8.7 , 9 .0, 9.7 , 9.7 , 10.6 , 11.5 , 11.6 , 11.8}

(a)

Construct a stem-and-leaf display of the data as follows:

5 | 7

6 | 2  3  5  8  8

7 | 0  0  2  3  4  6  7  7  8  8  9

8 | 1  2  7

9 | 0  7  7

10 | 6

11 | 5  6  8

The representative strength value is the mid-value.

The mid-value is: 7.7

Thus, the representative strength value is 7.7.

(b)

No, the data does not appear to be highly concentrated about the representative value or rather spread out.

As we take the stem-and-leaf plot into consideration we observe that most of the observations are concentrated towards the right of the graph.

So, the data is right or positively skewed.

(c)

No, there doesn't appear to be any outlying strength values.

This is because all the values are closer to each other and none of the observations are too extreme.

(d)

The number of observations more than 10 MPa is, 4.

Total number of observations, 27.

Compute the proportion of strength observations that exceed 10 MPa as follows:

Thus, the proportion of strength observations that exceed 10 MPa is 15%.