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Data Analysis

Data Analysis. Sugar Content in Beverages. Step 1 – The Calibration Curve. Page 2 of the procedure presents a table of “Percent Sugar” vs. “Density at 20 °C.” This is data obtained from previous experiments. Question: What kind of experiment would you design to produce a similar table?.

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Data Analysis

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  1. Data Analysis Sugar Content in Beverages

  2. Step 1 – The Calibration Curve • Page 2 of the procedure presents a table of “Percent Sugar” vs. “Density at 20°C.” • This is data obtained from previous experiments. • Question: What kind of experiment would you design to produce a similar table?

  3. Step 1 – The Calibration Curve • The data from this table will give us the experimental value of the sugar content of the beverages tested. • We use graph paper to make a plot of the data.

  4. Step 1 – The Calibration Curve Use the entire length and width of the graph paper to make the graph. 1.080 Next, plot the data given in the data table. 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  5. Step 1 – The Calibration Curve 1% sugar has a density of 1.002 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  6. Step 1 – The Calibration Curve 5% sugar has a density of 1.018 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  7. Step 1 – The Calibration Curve 10% sugar has a density of 1.038 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  8. Step 1 – The Calibration Curve 15% sugar has a density of 1.059 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  9. Step 1 – The Calibration Curve 20% sugar has a density of 1.081 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  10. Step 1 – The Calibration Curve Next, we draw the “best fit” straight line through the data points. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  11. Step 2 – Experimental Sugar Content In Step 2 of the Data Analysis, we get an experimental estimate of the percent sugar of the beverages using the graph. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  12. Step 2 – Experimental Sugar Content We use our experimental density data to get our estimate. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  13. Step 2 – Experimental Sugar Content For example, suppose we determined the density of Pepsi to be 1.0032 g/mL. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  14. Step 2 – Experimental Sugar Content We draw a line from the “Density” axis, at a value of 1.0032 g/mL, over to our calibration curve. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  15. Step 2 – Experimental Sugar Content Then we draw a line down from the calibration curve to the “Percent Sugar” axis. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  16. Step 2 – Experimental Sugar Content Then, we read off the value of the percent sugar in Pepsi as about 8.0%. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  17. Step 2 – Experimental Sugar Content We do the same thing for each beverage density value. 1.080 1.060 Density (g/mL) 1.040 1.020 1.000 1% 5% 10% 15% 20% Percent Sugar

  18. Step 3 – Calculated Sugar Content • Step 3 of the Data Analysis uses the nutritional labels of the beverages to give us a calculated value of the sugar content of the beverages. • Pepsi has 26 g of sugar in 222 mL of beverage. • This is (26 g sugar/222 mL Pepsi) • Pepsi has a measured density of 1.0032 g/mL. • This is (1.0032 g Pepsi/1 mL Pepsi)

  19. Step 3 – Calculated Sugar Content • We calculate the sugar content of the beverage by • taking the nutritional data (26 g sugar/222 mL Pepsi) and • dividing it by the measured density (1.0032 g Pepsi/1 mL Pepsi)

  20. Step 3 – Calculated Sugar Content 26 g sugar/222 mL Pepsi = 1.0032 g Pepsi/1 mL Pepsi 26 g sugar 26 g sugar 1.0032 g Pepsi 1.0032 g Pepsi ÷ ÷ 222 mL Pepsi 222 mL Pepsi 1 mL Pepsi 1 mL Pepsi 26 g sugar 26 g sugar 26 g sugar 26 g sugar 1 mL Pepsi 1 × × 222.7 g Pepsi 222 mL Pepsi 222×1.0032 g Pepsi 222 1.0032 g Pepsi 1.0032 g Pepsi 26 g sugar 1 mL Pepsi × 222 mL Pepsi 1.0032 g Pepsi 26 g sugar 1 × = 0.116 g sugar/g Pepsi 222 1.0032 g Pepsi 26 g sugar Calculated percent sugar = (0.116 g sugar/g Pepsi)×100% = 11.6 % sugar 222×1.0032 g Pepsi

  21. Step 3 – Calculated Sugar Content • The calculated percent sugar for Pepsi is 11.6%.

  22. Step 4 – Percent Error • The calculated percent sugar for Pepsi is 11.6%. • This is different from the measured percent sugar we determined using the calibration curve. • We measured 8.0% sugar.

  23. Step 4 – Percent Error • The percent error is an indication of the magnitude of the error. |calculated value – experimental value| |11.6% – 8.0%| % error = % error = ×100% ×100% calculated value 11.6% = 31%

  24. Review of Data • The measured percent sugar from the calibration curve is 8.0%. • The calculated percent sugar from the nutritional data is 11.6%. • The percent error is 31%.

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