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?
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.
Step 1 – The Calibration Curve Density (g/mL) Percent Sugar 1% 5%10%15%20% Use the entire length and width of the graph paper to make the graph. Next, plot the data given in the data table.
Step 1 – The Calibration Curve Density (g/mL) Percent Sugar 1% 5%10%15%20% % sugar has a density of g/mL.
Step 1 – The Calibration Curve Density (g/mL) Percent Sugar 1% 5%10%15%20% % sugar has a density of g/mL.
Step 1 – The Calibration Curve Density (g/mL) Percent Sugar 1% 5%10%15%20% % sugar has a density of g/mL.
Step 1 – The Calibration Curve Density (g/mL) Percent Sugar 1% 5%10%15%20% % sugar has a density of g/mL.
Step 1 – The Calibration Curve Density (g/mL) Percent Sugar 1% 5%10%15%20% % sugar has a density of g/mL.
Step 1 – The Calibration Curve Density (g/mL) Percent Sugar 1% 5%10%15%20% Next, we draw the “best fit” straight line through the data points.
Step 2 – Experimental Sugar Content Density (g/mL) Percent Sugar 1% 5%10%15%20% In Step 2 of the Data Analysis, we get an experimental estimate of the percent sugar of the beverages using the graph.
Step 2 – Experimental Sugar Content Density (g/mL) Percent Sugar 1% 5%10%15%20% We use our experimental density data to get our estimate.
Step 2 – Experimental Sugar Content Density (g/mL) Percent Sugar 1% 5%10%15%20% For example, suppose we determined the density of Pepsi to be g/mL.
Step 2 – Experimental Sugar Content Density (g/mL) Percent Sugar 1% 5%10%15%20% We draw a line from the “Density” axis, at a value of g/mL, over to our calibration curve.
Step 2 – Experimental Sugar Content Density (g/mL) Percent Sugar 1% 5%10%15%20% Then we draw a line down from the calibration curve to the “Percent Sugar” axis.
Step 2 – Experimental Sugar Content Density (g/mL) Percent Sugar 1% 5%10%15%20% Then, we read off the value of the percent sugar in Pepsi as about 8.0%.
Step 2 – Experimental Sugar Content Density (g/mL) Percent Sugar 1% 5%10%15%20% We do the same thing for each beverage density value.
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 g/mL. – This is ( g Pepsi/1 mL Pepsi)
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 ( g Pepsi/1 mL Pepsi)
Step 3 – Calculated Sugar Content 26 g sugar/222 mL Pepsi g Pepsi/1 mL Pepsi = 26 g sugar 222 mL Pepsi ÷ g Pepsi 1 mL Pepsi 26 g sugar 222 mL Pepsi ÷ g Pepsi 1 mL Pepsi 26 g sugar 222 mL Pepsi × 1 mL Pepsi g Pepsi 26 g sugar 222 mL Pepsi × 1 mL Pepsi g Pepsi 26 g sugar 222 × g Pepsi 26 g sugar 222 × g Pepsi 26 g sugar 222× g Pepsi 26 g sugar 222× g Pepsi 26 g sugar g Pepsi = g sugar/g Pepsi Calculated percent sugar = (0.116 g sugar/g Pepsi)×100%= 11.6 % sugar
Step 3 – Calculated Sugar Content The calculated percent sugar for Pepsi is 11.6%.
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.
Step 4 – Percent Error The percent error is an indication of the magnitude of the error. % error = |calculated value – experimental value| calculated value ×100% error = |11.6% – 8.0%| 11.6% ×100% = 31%
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%.