A mathematical statement that uses an equal sign to say that two things are the same
Answer:
(a)
![\bar x = 0.0075](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%200.0075)
![s = 0.0049](https://tex.z-dn.net/?f=s%20%3D%200.0049)
(b)
B. The sample is too small to make judgments about skewness or symmetry.
Step-by-step explanation:
Given:
![n = 8](https://tex.z-dn.net/?f=n%20%3D%208)
![\begin{array}{ccccccccc}{} & {S} & {u} & {b} &{j} & {e} & {c} & {t} & {s} &{Operator} & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {1} & 1.326 & 1.337 & 1.079 & 1.229 & 0.936 & 1.009 & 1.179 & 1.289 & 2 & 1.323 & 1.322 & 1.073 & 1.233 & 0.934 & 1.019 & 1.184 & 1.304 \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccccccccc%7D%7B%7D%20%26%20%7BS%7D%20%26%20%7Bu%7D%20%26%20%7Bb%7D%20%26%7Bj%7D%20%26%20%7Be%7D%20%26%20%7Bc%7D%20%26%20%7Bt%7D%20%26%20%7Bs%7D%20%26%7BOperator%7D%20%26%20%7B1%7D%20%26%20%7B2%7D%20%26%20%7B3%7D%20%26%20%7B4%7D%20%26%20%7B5%7D%20%26%20%7B6%7D%20%26%20%7B7%7D%20%26%20%7B8%7D%20%26%20%7B1%7D%20%26%201.326%20%26%201.337%20%26%201.079%20%26%201.229%20%26%200.936%20%26%201.009%20%26%201.179%20%26%201.289%20%26%202%20%26%201.323%20%26%201.322%20%26%201.073%20%26%201.233%20%26%200.934%20%26%201.019%20%26%201.184%20%26%201.304%20%5C%20%5Cend%7Barray%7D)
Solving (a):
First, calculate the difference between the recorded TBBMC for both operators:
![\begin{array}{ccccccccc}{} & {S} & {u} & {b} &{j} & {e} & {c} & {t} & {s} &{Operator} & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {1} & 1.326 & 1.337 & 1.079 & 1.229 & 0.936 & 1.009 & 1.179 & 1.289 & 2 & 1.323 & 1.322 & 1.073 & 1.233 & 0.934 & 1.019 & 1.184 & 1.304 &{|1 - 2|} &0.003 & 0.015 & 0.006 & 0.004 & 0.002 & 0.010 & 0.005 & 0.015 \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccccccccc%7D%7B%7D%20%26%20%7BS%7D%20%26%20%7Bu%7D%20%26%20%7Bb%7D%20%26%7Bj%7D%20%26%20%7Be%7D%20%26%20%7Bc%7D%20%26%20%7Bt%7D%20%26%20%7Bs%7D%20%26%7BOperator%7D%20%26%20%7B1%7D%20%26%20%7B2%7D%20%26%20%7B3%7D%20%26%20%7B4%7D%20%26%20%7B5%7D%20%26%20%7B6%7D%20%26%20%7B7%7D%20%26%20%7B8%7D%20%26%20%7B1%7D%20%26%201.326%20%26%201.337%20%26%201.079%20%26%201.229%20%26%200.936%20%26%201.009%20%26%201.179%20%26%201.289%20%26%202%20%26%201.323%20%26%201.322%20%26%201.073%20%26%201.233%20%26%200.934%20%26%201.019%20%26%201.184%20%26%201.304%20%26%7B%7C1%20-%202%7C%7D%20%260.003%20%26%200.015%20%26%200.006%20%26%200.004%20%26%200.002%20%26%200.010%20%26%200.005%20%26%200.015%20%5C%20%5Cend%7Barray%7D)
The last row which represents the difference between 1 and 2 is calculated using absolute values. So, no negative entry is recorded.
The mean is then calculated as:
![\bar x = \frac{\sum x}{n}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B%5Csum%20x%7D%7Bn%7D)
![\bar x = \frac{0.003 + 0.015 + 0.006 + 0.004 + 0.002 + 0.010 + 0.005 + 0.015}{8}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B0.003%20%2B%200.015%20%2B%200.006%20%2B%200.004%20%2B%200.002%20%2B%200.010%20%2B%200.005%20%2B%200.015%7D%7B8%7D)
![\bar x = \frac{0.06}{8}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B0.06%7D%7B8%7D)
![\bar x = 0.0075](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%200.0075)
Next, calculate the standard deviation (s).
This is calculated using:
![s = \sqrt{\frac{\sum (x - \bar x)^2}{n}}](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum%20%28x%20-%20%5Cbar%20x%29%5E2%7D%7Bn%7D%7D)
So, we have
![s = \sqrt\frac{(0.003 - 0.0075)^2 + (0.015 - 0.0075)^2+ (0.006- 0.0075)^2+ ....... + (0.005- 0.0075)^2+ (0.015- 0.0075)^2 }{8}](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%5Cfrac%7B%280.003%20-%200.0075%29%5E2%20%2B%20%280.015%20-%200.0075%29%5E2%2B%20%280.006-%200.0075%29%5E2%2B%20.......%20%2B%20%280.005-%200.0075%29%5E2%2B%20%280.015-%200.0075%29%5E2%20%7D%7B8%7D)
![s = \sqrt\frac{0.00019}{8}](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%5Cfrac%7B0.00019%7D%7B8%7D)
![s = \sqrt{0.00002375](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%7B0.00002375)
Solving (b):
Of the given options (A - E), option B is correct because the sample is actually too small
Answer: I think A 1,220 (I'm not sure)
Step-by-step explanation: