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Question 1

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A manager of a factory purchases a large number of sheets of aluminium, all of them longer than 100 cm in length. Each piece is then cut so that it is 100 cm long. The length of a sample of the off-cuts, in cm, resulting from cutting the lengths to size are given below:
5,2 6,6 3,5 8,9 7,5
7,3
Using the data above:
Calculate the standard deviation of the lengths rounded to 1 decimal place
0 3,6
о 3.7
O 1.9
о 1.7

Answer 1

To calculate the standard deviation of the lengths, we can follow these steps:

Calculate the mean (average) of the lengths.

Calculate the difference between each length and the mean.

Square each difference.

Calculate the average of the squared differences.

Take the square root of the average of the squared differences to obtain the standard deviation.

Let's perform these calculations using the given data:

Lengths: 5.2, 6.6, 3.5, 8.9, 7.5, 7.3

Step 1: Calculate the mean:

Mean = (5.2 + 6.6 + 3.5 + 8.9 + 7.5 + 7.3) / 6 = 38 / 6 = 6.3

Step 2: Calculate the difference between each length and the mean:

5.2 - 6.3 = -1.1

6.6 - 6.3 = 0.3

3.5 - 6.3 = -2.8

8.9 - 6.3 = 2.6

7.5 - 6.3 = 1.2

7.3 - 6.3 = 1

Step 3: Square each difference:

(-1.1)^2 = 1.21

(0.3)^2 = 0.09

(-2.8)^2 = 7.84

(2.6)^2 = 6.76

(1.2)^2 = 1.44

(1)^2 = 1

Step 4: Calculate the average of the squared differences:

(1.21 + 0.09 + 7.84 + 6.76 + 1.44 + 1) / 6 = 18.34 / 6 = 3.06

Step 5: Take the square root of the average of the squared differences:

Standard deviation = √3.06 ≈ 1.7 (rounded to 1 decimal place)

Therefore, the standard deviation of the lengths is approximately 1.7.