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
Use the entire length and width of the
graph paper to make the graph.
Density (g/mL)
1.080
Next, plot the data given in the data table.
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
Step 1 – The Calibration Curve
1% sugar has a density of 1.002 g/mL.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
Step 1 – The Calibration Curve
5% sugar has a density of 1.018 g/mL.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
Step 1 – The Calibration Curve
10% sugar has a density of 1.038 g/mL.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
Step 1 – The Calibration Curve
15% sugar has a density of 1.059 g/mL.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
Step 1 – The Calibration Curve
20% sugar has a density of 1.081 g/mL.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
Step 1 – The Calibration Curve
Next, we draw the “best fit” straight
line through the data points.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
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.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
Step 2 – Experimental Sugar Content
We use our experimental density data
to get our estimate.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
Step 2 – Experimental Sugar Content
For example, suppose we determined
the density of Pepsi to be 1.0032 g/mL.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
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.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
Step 2 – Experimental Sugar Content
Then we draw a line down from the
calibration curve to the “Percent
Sugar” axis.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
Step 2 – Experimental Sugar Content
Then, we read off the value of the
percent sugar in Pepsi as about 8.0%.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
Step 2 – Experimental Sugar Content
We do the same thing for each
beverage density value.
Density (g/mL)
1.080
1.060
1.040
1.020
1.000
1%
5%
10%
Percent Sugar
15%
20%
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)
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)
Step 3 – Calculated Sugar Content
26 g sugar/222 mL Pepsi
1.0032 g Pepsi/1 mL Pepsi
26 g sugar
1.0032 g Pepsi
÷
=
222 mL Pepsi
1 mL Pepsi
26 g sugar
1.0032 g Pepsi
÷
222 mL Pepsi
1 mL Pepsi
26 g sugar
1 mL Pepsi
×
222 mL Pepsi 1.0032 g Pepsi
26 g sugar
1 mL Pepsi
×
222 mL Pepsi 1.0032 g Pepsi
26 g sugar
1
×
222
1.0032 g Pepsi
26 g sugar
1
×
222
1.0032 g Pepsi
26 g sugar
222×1.0032 g Pepsi
26 g sugar
222×1.0032 g Pepsi
26 g sugar
222.7 g Pepsi = 0.116 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.
|calculated value – experimental value|
% error =
×100%
calculated value
|11.6% – 8.0%|
% error =
×100% = 31%
11.6%
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%.