The pH of a solution is measured eight times by one operator using the same instrument. She obtains the following data: 7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.17, and 7.18. (a) Calculate the sample mean. Round your answer to 3 decimal places. (b) Calculate the sample variance. Round your answer to 6 decimal places. (c) Calculate the sample standard deviation. Round your answer to 3 decimal places. (d) Which of the following are potential major sources of variability in the experiment

(a)7.185

(b)0.000371

(c) 0.019

(d)Sample variance and Sample standard deviation

Step-by-step explanation:

We are given the following sample data.

7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.17, 7.18.

(a) Calculate the sample mean. Round your answer to 3 decimal places.

The formula for sample mean =

Sum of terms/Number of terms

= 7.15 + 7.20+ 7.18+7.19+7.21+7.20+7.17+ 7.18/8

= 57.48/8

= 7.185

(b) Calculate the sample variance. Round your answer to 6 decimal places.

The formula for sample Variance =

(x - mean)²/n - 1

n = 8

Sample variance = (7.15 - 7.185)² + (7.20-

7.185)²+ (7.18 -7.185)² + (7.19 -7.185)² + (7.21 - 7.185)² + (7.20 - 7.185)² + (7.17 - 7.185)² + (7.18 - 7.185)² /8 - 1

= 0.001225 + 0.000225+ 0.000025+ 0.000025 + 0.000625 + 0.000225 + 0.000225 + 0.000025/7

= 0.0026/7

= 0.000371428571

Approximately to 6 decimal places = 0.000371

(c) Calculate the sample standard deviation. Round your answer to 3 decimal places.

The formula for Sample Standard Deviation = √Sample variance

= √0.000371428571

= 0.01927248223

To 3 decimal places = 0.019

(d) Which of the following are potential major sources of variability in the experiment

Sample variance

Sample standard deviation

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>