Measurements Statistics And Significant Digits Biology Essay

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The question in the experiment carried out was How accurate can you measure. In order to answer this question, a hypothesis was formed based on the purposes of this lab activity. The hypothesis stated was the following: "If we measure an object, then the accuracy depends on the instrument, because the manufacturer of the instrument calibrated that instrument to certain accuracy."

Pre-laboratory /preparatory questions

If you are using a graduated cylinder whose smallest division is 0.1 mL, to what degree of precision should you report liquid volumes?

Students should report liquid volumes to a degree of precision of +/- 0.01.

A stack of five CDs is 1.6 cm tall. What is the average thickness of each disk? To the nearest whole number, how many disks will be in a stack 10 cm tall?

1.6/5=0.32

The average thickness of each CD is 0.32 centimeters.

10/0.32= 31.25

In a stack of 10 centimeters tall there would be 31 CDs.

What is a meniscus; what role does it play in the correct reading of liquid volumes?

"The meniscus is the curve that is formed in the surface of a liquid close to the surface of another liquid. It is caused by surface tension (Wikipedia, 2012)".

Given a set of data, the mean of these numbers is its average. To find the mean, add all the numbers given in the data and divide by the amount of numbers given. The median is the middle number of the data, when it is ordered from least to greatest. If there are two numbers in the middle, find the average of those two numbers and that will be the median. Mode is the most repeated number in the data. Range is the difference between the greatest and lowest number arranged from least to greatest. Scientific notation is a way to express numbers using a base ten. It helps when working with large and small numbers. Significant digits are used in scientific work to make it easier to scientists. There are rules to follow when writing scientific digits. Examples:

30.2, has three significant digits.

100, has one significant digits.

100., has three significant digits.

0.0054, has two significant digits

Celsius

Kelvin

Fahrenheit

What is the boiling point of water?

100°C

373.15K

212°F

What is the freezing point of water?

0.°C

273.15K

32.°F

What is the normal body temperature?

37.°C

310.15K

98.6°F

Complete the chart

-40C

233.15K

-40°F

- 273.15°C

0K

-459.67°F

210°C

63.15K

- 346°F

Theoretical Framework

In the experiment students had the opportunity to manipulate lab instruments and terms to which they are unfamiliar such as the triple beam balance, significant digits, and uncertainty. The triple beam balance is a scale to measure the mass of lab samples. Significant digits are all the non-zero digits, also are the zeros that occur between significant digits. The uncertainty shows the margin of error acceptable in measuring. (Wikipedia, 2012)

Materials

Specials rulers (1=feet, 2=inches, 3&4 are in cm)

Graduated cylinders (3) 100, 50, 10 mL

Triple-beam balance

Beakers (3) 150mL

Erlenmeyer flask (4) 125mL

Tap water

Ice

Thermometer, -20°C to 110°C (4)

Hot plate

Bag of M&M candy

Procedure

In the first step, I measured the width and the length of the biology books. I had to use four different rulers. One of them had the measurement of 1 foot. The second one had the measures in inches. The third and forth one I had to measure it in cm. After measuring I had to calculate the perimeter and the area of each measurement.

In the second part of the lab, I had to look at three graduated cylinders. Each of these cylinders had different volume capacities. Then I recorded the nominal capacity, volume of the liquid and the uncertainty in table B.

The step three of this lab consisted in weighting 3 beaker three times. Each beaker had different volume which also had different weight. I had to weight each beaker in the three triple beam balances, set on the table. After I weighted the three beakers in every balance I had to find the average weight of the three weights.

The forth step of the lab was to measure the temperature of 4 flasks. Two of those flasks were on the hot plate and the other two were on a side. I was expected to measure the temperature in Celsius and then I had to convert it in Kelvin. After I had the temperatures I recorded my data on table C.

The fifth step of this lab experiment consisted in measuring a full bag of M&M and record the data in table E. I also had to weight the bag of M&M empty. Then had to separate the candy into colors and count how much of a kind there were. After that I had to find the percentage of each color in my bag. After that I had to determine the class totals in colors in each bag.

Results

Data Table - Part A

Ruler number

Length

Width

Length

Width

Perimeter

Area

1

+/-0.9 ft

+/-0.7ft

27.43cm

21.33 cm

97.52 cm

585.0819cm2

2

11in

8.5in

27.94cm

21.59 cm

110.74 cm

603.2246 cm2

3

27.4 cm

21.3cm

27.4cm

21.3 cm

97.4 cm

583.62 cm2

4

27.40 cm

31.30cm

27.40cm

21.30 cm

97.40cm

583.620 cm2

(Online Conversions, 2012)

Data Table - Part B

Graduated cylinder

Nominal Capacity

Volume of Liquid

Uncertainty ±

1

10mL

7.02mL

+/- 0.01

2

50mL

31.2mL

+/- 0.1

3

100mL

83mL

+/- 0.1

Data Table part C

Jar

Weight 1

Weight 2

Weight 3

Average

Uncertainty +/-

1 red

131.05

131.56

131.58

131.39

0.01g

2 yellow

157.04

157.55

157.55

157.38

0.01g

3 blue

110.05

114.02

114.03

112.7

0.01g

Data Table - Part D

Beaker (-20°C to 110°C)

Temperature Celsius

Temperature Kelvin

Uncertainty ±

1

101°C

383.15K

0.1

2

22.5°C

295.65K

0.01

Beaker (-20°C to 110°C)

Temperature Celsius

Temperature Kelvin

Uncertainty ±

1

102.4°C

375.55K

0.01

2

23°C

296.15K

0.1

Data Table - Part E

Color of M&M

Number in bag

Percent in bag

Class totals

Brown

0

0

14

Yellow

2

11%

14

Red

3

16%

25

Green

4

21%

41

Blue

3

16%

29

Orange

7

36%

48

TOTALS

19

100%

171

Weight with the M&M's 17.04 grams

Weight empty 0.04

j

Mode

Median

Mean

Range

brown

0

0

0

1

1

1

2

3

4

0,1

1

1.3333

4

yellow

0

0

1

2

2

2

3

3

3

3

2

1.7777

3

Red

0

1

1

2

3

4

4

4

6

4

3

2.7777

6

green

1

3

3

4

4

5

6

7

7

3,4,7

4

4.4444

6

blue

2

3

3

3

3

3

4

4

5

3

3

3.3333

3

orange

3

3

4

5

6

6

7

7

7

7

6

5.3333

4

Analysis

The ruler 4 gave me the most precise measurement because the more divisions a ruler has the easier it is. The ruler 1 gave the most un-precise measure. When I was measuring the book the cm one made it easier to record my data, but the ruler 1 was a little bit difficult. It occurs because the 1 foot ruler is an actual estimation of the book, but the cm is the exact measurement to the book.

The most common explanation for a decrease of volume in a graduated cylinder is evaporation of the water in the container. The explanation I could give is the meniscus, which is the curve you see when watching a graduated cylinder filled with water.

The 100mL container gave me the most precise reading of the graduated cylinders, because it was the most visible and had more space between lines.

Something that might cause an unavoidable error is that fact that the balances say they are balanced but are still moving. Another unavoidable error is that in between the changing of the balance you accidentally pour out a little bit of liquid inside the container.

You know when a container has salt when the temperature is lower than the other one that does not have salt.

I think my percent differs from everybody else because the bags have different amount of M&Ms in each of the bags. The number of the M&M in a bag is not always the same.

Conclusion

The lab experiment carried out involved activities to gain experience in measurements, using significant digits and scientific notation in real life situations. At the same time, students had the opportunity to calculate mean, median, mode, and range given a set of data. The lab activity was conducted with the purpose of exposing students to basic concepts and instruments used in Science. It was intended to find out how accurate students can measure. As a hypothesis, students proposed that when measuring an object, the accuracy depends on the instrument, due to the fact that the manufacturers calibrate it to certain accuracy. It involved simple processes such as using different rulers to measure the length and the width of the biology book, measuring temperature of liquids, using beakers and the tripod beam balance for finding the weight of the liquids, and the graduated cylinders to figure out the volume of each container. Finally, students had a fun opportunity to find the mean, median, mode, and range of units of M&Ms. As part of the results; we were able to observe that the most calibrated instruments were the ones with the most accurate measures. Therefore, the hypothesis was accepted because it was proved that the level of accuracy depended on the manufacturer and how they calibrate their instruments.

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