HERE

Algebra 2 – Stats WS 1
Data Analysis
Name:
Per:
Background: One of the most important steps that a scientist completes during an experiment is data
processing and presentation. Data can be analyzed by the presentation of the data in table format (data
table), or the processing of that data through graphical manipulation to visually discern the differences
in the variables tested.
Table 1: Growth of eight plants in a three-week period
Amount of
Amount of Water Height Week
Light per day
per day
1 in cm
Plant 1
0 hours
¼ cup
0 cm
Plant 2
0 hours
1 cup
0 cm
Plant 3
4 hours
¼ cup
1 cm
Plant 4
4 hours
1 cup
0.5 cm
Plant 5
8 hours
¼ cup
1.5 cm
Plant 6
8 hours
1 cup
1 cm
Plant 7
16 hours
¼ cup
1 cm
Plant 8
16 hours
1 cup
1.5 cm
Height Week
2 in cm
0 cm
0 cm
3 cm
1 cm
4 cm
3 cm
2 cm
5 cm
Height Week
3 in cm
0 cm
0 cm
6 cm
1.5 cm
8 cm
6 cm
3 cm
10 cm
1.
a. In this plant growth experiment, what were the two variables tested? Are they categorical or
quantitative?
1a. The two variables tested are amount of light and the amount of water given to a plant.
The variables are quantitative (as opposed to categorical) because the categories are
numerical. If the variables were categorical, one could be testing, for example, how growth
from a plant with equal amounts of water, but some with sugar in the water, others with salt
in the water, another with baking soda in the water, etc.
b.
What conclusions can you draw in regards to the amount of light a plant was exposed to and
how tall the plant grew?
1b. It appears that the more light a plant is exposed to, the more the plant grows. Perhaps 16
hours of light is too much and 8 hours of light per day is better since one plant with 8 hours
per day grew better than one of 16 hours per day plant. Further investigation would be
required to get to the bottom of this question.
c. What conclusions can you draw in regards to the amount of water given to a plant and how tall
the plant grew?
1c. It appears that a ¼ cup is better at 4 hrs. and at 8 hrs. Once the plant begins to receive 16
hours of light, 1 cup is better. Maybe this has something to do with evaporation and light?
Also since our sample size is so small it is difficult to find exact causation.
2. When given categorical data, what graphs are the most appropriate to use? Graph the data given in
Table 2.
Table 2: Average rainfall in Willamette Valley
Month Jan. Feb. Mar. April May June July Aug. Sept. Oct. Nov. Dec.
Rainfall
15
21
28
24
16
8
2
1
2
3
5
10
(ml)
2a. Create a bar graph or pie chart. We can do this because the
data we are working with is categorical (months are categories) as
opposed to numbers.
3. About 1.6 million first-year students enroll in colleges and universities each year. (a) What are the
three most popular and three least popular majors? The pie chart displays data on the percent of firstyear students who plan to major in several discipline areas. Estimate what percent of first-year
students plan to major in (b) business and (c) social science?
3a. Most popular: Business, Professional, Arts
and Humanities
Least popular: Technical, Physical Sciences,
Biological Sciences
3b. Business comprises about 18-20% of first year
students.
3c. Social Science comprises about 10-12%
4. The following dotplot shows the difference (highway–city) in EPA mileage ratings for each of the 24
car models randomly selected from the Kelley Blue-Book Listings.
(a) Explain what the dot above 12 represents.
4a. The dot above 12 represents a single car where the difference between city and highway
mileage is 12 miles/gallon.
(b) What does the graph tell us about fuel economy in the city versus on the highway for these
car models? Be specific.
4b. The graph tells us that highway mileage is better than city mileage. Except for the Prius…
5. The return on a stock is the change in its market price plus any dividend payments made. Total
return is usually expressed as a percent of the beginning price. The figure below shows a histogram
of the distribution of the monthly returns for all common stocks listed on U.S. markets over a 273month period. The extreme low outlier represents the market crash of October 1987, when stocks
lost 23% of their value in one month.
(a) What percent return on common stocks is
most common? Explain.
5a. Between 0 and 2.5% is the most common
return on stocks. This is where the histogram is
tallest.
(b) Approximately what were the worst and
strongest monthly returns?
5b. Strongest : 10-12.5% return
Worst : -22.5-25% return
(c) A return less than zero means that stocks lost value in that month. About what percent of all
months had returns less than zero?
5c. Slightly less than half of all months had returns less than zero.