Solutions Derived From Working Drawings, Plans & Documents

Task1

Strength (N/mm2) 10 11 12 13 14 15 16 17 18 19 20

Frequency 01 02 03 06 08 11 06 05 03 04 02

Unit Value: 1.0 N/mm2 Chosen Value: 15 N/mm2

Minimum Strength of the concrete from the samples: 10 N/mm2

Maximum Strength of the concrete from the samples: 20 N/mm2

To calculate the mean of the results we must use the formula:

_X = ∑ χf ∑f

χ Xc f Xcf Xc2f

10 -5 1 -5 25

11 -4 2 -8 32

12 -3 3 -9 27

13 -2 6 -12 24

14 -1 8 -8 8

15 0 11 0 0

16 1 6 6 6

17 2 5 10 20

18 3 3 9 27

19 4 4 16 64

20 5 2 10 50

Total: 51 9 283

_

Now Xc = ∑cf = 9 = 0.176470588

∑f 51

_

Therefore X = 15 + (0.176470588 x 1.0) = 15.176470588 N/mm2

Average strength of the concrete samples: 15.176470588 N/mm2

To calculate the Standard Deviation we must use the formula:

_∂c = ∑ X2f Ð'- (Xc) 2 ∑f

_

∂c = ∑ X2f Ð'- (Xc) 2

∑f

= 283 Ð'- (0.176470588) 2

51

= 5.549019608 Ð'- 0.031141868

= 5.51787774

= 2.349016262

Therefore ∂ = 2.3490 x unit size = 2.3490 x 1.0 = 2.3490 N/mm2

Rough check for ∂

Range = 10 is the lowest value Range = 20 - 10

20 is the highest value = 10

Number of values = 11. Take away the first and last value (10 and 20), and left with 9 values.

Approximate ∂ = 10 = 1.111ׂ

9

Check approximate values Rough = 1.111ׂ

Actual = 2.349

As the answers are only 1.2 decimals apart, I am confident that I have the correct answer.

Calculate the probability of the concrete strength being less than 14 N/mm2.

M (Mean) =