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6) Calculate the average and standard deviation for the following set of calibration data: 3.8842, 3.8611, 3.8263, 3.8191, 3.8945, 3.8916, 3.8511, 3.8651
) The following data were used to calibrate a spectrometer. Graph the data and answer the questions regarding the resulting line. Known Wavelength Spectrometer Reading (nm) 388.9 488.6 501.6 587.6 667.8 706.5 (absorbance units) 3.47 4.43 4.56 5.38 6.15 6.52 Q1. Add a best-fit line and calculate the equation for that line. Q2. You have collected some more data using the above spectrometer. Use either the graph or the equation of the line to correct the data you have collected. Experimental Corrected Spectrometer Reading Wavelength (absorbance units) 5.82 4.27 4.00 6.18 (nm)
math   Statistics-And-Probability   
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Answer #1

6.) Average (Xbar) = Sum of data / Number of data = 3.8616

    Standard deviation ( σ ) = ⎷ ∑(xi−Xbar)2 / (n−1)

data 3.8842 3.8611 3.8263 3.8191 3.8945 3.8916 3.8511 3.8651 data-mean 0.0226 0.0005 -0.0353 0.0425 0.0329 0.03 0.0105 0.0035 (data - mean) 0.00051076 2.5Е-7 0.00124609 0.00180625 0.00108241 0.0009 0.00011025 1.225E-5

= ∑(xi−Xbar)2 = 0.0057

= √0.0057 / (8−1) ≈ 0.0285

Q1

For Linear Equation: y = ax + b, formula to calculate the a and b is:
    a.png
    b.png
Where:
   x: mean of x
   y: mean of y
   xi: the ith number of x
   yi: the ith number of y
   n:total numbers of x or y

Line of best fit -

6.5 5.9 5.3 4.7 4.1 3.5 516 579 643 706 389 452

Intercept : -0.259614

Slope: 0.009598

Line of Best Fit : y = 0.009598x - 0.259614

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