Question

5A1: Analyzing Lab Results

In the table below are the results from four analytical labs, each of which analyzed the same soil sample for its benzene content. The actual concentration of benzene in the soil is 25 ppb.

Reported Concentration of Benzene in a Soil Sample (ppb)
Replicate	Lab A	Lab B	Lab C	Lab D
1	25	19	25	28
2	29	29	25	27
3	21	30	27	27
4	23	16	25	29
5	27	16	25	29
6	22	21	24	27
7	27	16	28	26
8	20	29	26	27
9	30	26	25	28
10	25	30	27	27

1. Compare the four sets of data:
   1. Which lab do you think has the most accurate data?
   2. Which lab has the most precise data?
   3. Is it the same lab?
2. Using the formulas for average error and variance found in the Critical Thinking: Comparing Accuracy and Precision of Four Different Labs Lesson, calculate the accuracy and precision of each lab's data.
   1. Was your initial evaluation correct regarding which lab generated the most accurate and most precise data? Show your work.

Answer 1

1 Accuracy is defined as how close the measured value is compared to the true value.

Precision is defined as how close the measured values are compared to each other.

a) Lab C has the most accurate data because most of the values are 25 or close to 25.

b) Lab D has the most precise data because the difference between maximum and minimum measurement output is 3, which is lowest of all data set.

c) It is not the same lab.

2. For Lab A,

Average error is ,  AE =-1/10 = -0.01

AE = (25 - 25) + (29 - 25) + (21 - 25) + (23 - 25) + (27 – 25) + (22-25) + (27 – 25) + (20 - 25) + (30 – 25) + (25 -25) 10

To calculate variance we need to find the average output which is 24.9. Now the Standard deviation is,

SD = 3.38

24.9)2 + (27 – 24.9)2 + (22 – 24.9)2 + (27 – 24.9)2 + (20 – 24.9)2 + (30 – 24.9)2 + (25 – 24.9) SD= 10

Similarly For Lab B,

AE= -1.8

SD= 6.20

For Lab C,

AE = 0.7

SD = 1.25

For Lab D,

AE = 2.5

SD = 0.97

a) As we can see the average error is lowest for Lab C implying Lab C is most accurate. Standard deviation is lowest for Lab D implying Lab D is most precise.