Name: _________________________________
Mrs. Keller
G8 Science 1st 4th 5th
Date: __________________________________
C2 Significant Differences in Measurement
You must show your work. You may need to use a separate paper to do this!
When people conduct experiments (scientific, or otherwise), how can they be certain the results are accurate?
The short answer is that they can never be certain the results are accurate. This is why experiments are usually
performed multiple times, and then analyzed to determine the amount of the error. The error is estimated by
calculating the largest difference between the average and a measured value. Once you know the amount of
error, it can be used to determine whether two results can be considered the same. If two measurements or
results differ by an amount that is less than or equal to the amount of error, they are considered to be the same.
One hot summer day, Dave and Chris decided to have a toy boat race in their little sisters’ wading pool. The
boats are identical, except for the sails. Dave’s boat has a rectangular sail, and Chris’ boat has a triangular sail.
They borrow their father’s timer to get the most accurate measurement possible. They raced the boats 5 times.
The results are given below.
Dave’s Boat ()
Time (seconds)
Chris’ Boat ()
Time (seconds)
0.528
0.525
0.532
0.530
0.530
0.529
0.526
0.520
0.533
0.529
Chris claims that since his boat won every race; that proves that his boat is the faster boat. Is this correct?
In order to determine if Chris’ claim is correct, you must decide if the times they have collected are significantly
different. If there is no significant difference between the times of the boats, then there is no evidence to support
that either boat is faster. Follow these steps to determine whether the difference is significant:
1. Find the average time it took each boat to complete the race course. Remember that the average is found by
dividing the sum of a data set by the number of items in the data set.
2. Find the amount of error for each data set. To calculate the error, find the greatest difference between the
average (found in #1) and any item in the data set.
2 of 3
a. Find the error for Dave’s boat: The difference between Dave’s boat’s average (0.530) and its slowest time
(0.533) is 0.003; the difference between the average and the fastest time (0.526) is 0.004. The largest
difference is 0.004, so the amount of error is ± 0.004.
b. Find the error for Chris’ boat: The difference between Chris’ boat’s average (0.527) and its slowest time
(0.530) is 0.003; the difference between the average and the fastest time (0.520) is 0.007. The largest
difference is 0.007, so the amount of error is ± 0.007.
3. Determine whether the difference is significant. First, find the difference between the averages for each set
of data. Here, the difference is found by subtracting the average time of Chris’ boat (0.527) from the
average time of Dave’s boat (0.530). Since 0.530 - 0.527 = 0.003, and 0.003 is not greater than the amount
of error found in #2, there is no significant difference between the two sets of data. In other words,
scientifically, the data are the same. It is impossible to determine which boat is faster.
A toy car and a toy truck of about the same size are started down identical ramps. The distance traveled by each
vehicle on each of four attempts is recorded below. Is it true that the truck will always travel farther than the
car? [Hint: follow the steps explained in the example]
Toy Car
Distance (m)
Toy Truck
(m)
1.57
1.77
1.45
1.90
1.55
1.85
1.48
2.00
Average
Average
Error
Error
2. The water pressure in the sinks at Sean’s house is constant. Sean wants to compare the water pressure in the
kitchen sink with the water pressure in the bathroom sink. He does this by recording the amount of time it
takes to fill a 1-cup measure with water from each sink. He performs this experiment a total of five times. Is
it possible to determine which sink has the greatest water pressure (fills the cup the quickest)? If so, which
sink has the greater water pressure?
Bathroom Sink
Time (seconds)
Kitchen Sink
Time (seconds)
3.42
3.12
3.50
3.15
3.45
3.12
3.49
3.10
3.47
3.13
Average
Average
Error
Error
3 of 3
3. After school one day, Antonio and Earnest were playing with a slingshot. Antonio’s mother said it would be
OK as long as they stayed in the back yard, and used only pencil erasers for ammunition. Antonio had a pink,
rectangular eraser, while Earnest had a smaller white, square one. The table below shows the distance traveled
by each eraser on 8 attempts. From only the given data, can you support (scientifically) Earnest’s claim that his
eraser will always go farther? Explain why or why not.
Antonio’s (pink) eraser
Distance (m)
Earnest’s (white) eraser
Distance (m)
3.12
3.20
3.20
3.75
3.55
3.22
3.04
3.05
3.48
3.58
3.60
3.63
3.16
3.18
3.35
3.41
4. While cleaning the kitchen sink one Saturday, Joanne noticed that her yellow sponge seemed to be a little
heavier than the pink one when they were both saturated with water, even though when the sponges were
dry, they seemed to have the same mass. Joanne found the mass of both sponges when they were dry. She
was right, each sponge had a mass of 31.50 grams. She saturated each sponge with plain water several
times, and recorded the data below. Does the data show (scientifically) that the yellow sponge absorbs more
water than the pink one? Explain why or why not.
Yellow Sponge
Mass (g)
Pink Sponge
Mass (g)
94.25
75.62
93.45
75.60
92.40
75.55
92.22
75.50
92.20
75.00
5. At Valley View Middle School, the girls’ 4  100 m relay team is set. Coach Davis still needs to determine
who the fastest runner is, so she can decide in what order they should run. The four girls on the relay team
run time trials twice each day for three days. Their times are given in the table below. Is it possible
(scientifically speaking) to determine who is the fastest? If so, which girl is the fastest?
Tara Time
(seconds)
Sammie Time
(seconds)
Joan Time
(seconds)
Lexy Time
(seconds)
12.70
12.59
13.02
12.77
12.99
12.45
13.01
12.80
13.00
12.40
13.00
12.78
12.88
12.60
12.95
12.99
12.75
12.54
13.05
12.94
12.80
12.42
13.11
12.90