MATH 208 2021 Midterm Exam
MATH 208 2021 Midterm Exam
Question 1 [50 points]
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my_Costco_list <- list(
tibble(Item = c("Milk", "Coffee", "Lettuce","Pants"),
Amount = c(4,1,2,2),
Location = c("Refrigerated","Cereal","Refrigerated","Clothes"))
both_lists <- list(Costco = my_Costco_list,
IGA = tibble(
Item = c("Chicken", "Yogurt", "Pizza"),
Amount = c(2,3,1),
Location = c("Meat","Dairy","Frozen")))
a. [15 pts] Consider code chunk Q1 and give the resulting output from the following R commands (or the
resulting error if one is produced):
i. my_Costco_list[2]
ii. my_Costco_list[[1]][2]
iii. my_Costco_list[[1]][2,2]
Solutions:
my_Costco_list[2]
my_Costco_list[[1]][2]
my_Costco_list[[1]][2,2]
b. [15 pts] Consider code chunk Q1 and answer the following multiple choice questions (please list all that
apply for each question):
i. Which of the following commands returns the result “Coffee”?
A.`both_lists$Costco$Item[2]`
B.`both_lists$Costco$Item[[2]]`
C.`both_lists[c(1,1,1,2)]`
D.`both_lists[[c(1,1,1,2)]]`
ii. The class of the object returned by both_lists[2] is a
A. atomic character vector
iii. The class of the object returned by both_lists[[2]]$Location is a
A. atomic character vector
(i) D only
(ii) C only
(iii) A only
c. [20 pts] Consider code chunk Q1 for the following questions:
i. [10 pts] Write a line of code that will change the Location column of the tibble in my_Costco_list
to an ordered factor where the order of the levels is in the following order: Clothes, Cereal,
Refrigerated.
ii. [10 pts] Write a line of code using your answer to part (i) to compute the minimum amount of
items (not the number of different items) required in each location.
my_Costco_list[[1]]<-my_Costco_list[[1]]%>%
mutate(Location=fct_relevel(Location,
c(“Clothes”,”Cereal”,”Refrigerated”)))
my_Costco_list[[1]]$Location
[1] Refrigerated Cereal Refrigerated Clothes
Levels: Clothes Cereal Refrigerated
my_Costco_list[[1]] %>% group_by(Location) %>%
summarize(min(Amount))
min(Amount)
Refrigerated 2
Question 2 [50 pts]
a. [15 marks] Please indicate which plot best summarizes the characeristic the characteristic (the name
of the plot, not the function):
i. Which plot best allows one to identify points that are outliers (i.e. far from the central location the
data): A: Boxplot B: Histogram?
ii. Which plot best allows one to assess the skew of the data: A: Boxplot B: Histogram?
iii. Which plot should be used to summarize the distribution of quantitative data that take on a large
number of unique values: A: Histogram B: Barplot?
iv. Which plot should be used to summarize the counts from different levels of a qualitative factor
variable: A: Histogram B: Barplot?
v. If we want to compare the central 50% of the values of a quantiative variable across multiple
levels of a separate qualitative variable, which plot should be used:
A. One boxplot for each group in the same plot
B. One boxplot for each group in a different plot
C. One hisotogram for each group in the same plot
D. One histogram for each group in a different plot?
Solutions:
Answer the parts (b), (c), and (d) below based on a dataset from Kaggle containing the prices of Hass
avocados over a period of over three years. The original dataset is used in the book “Introduction to Data
Analysis” and is available through the aida package in R (which you can install to access the data).
### You can install the aida package via:
### install.packages(“remotes”)
### remotes::install_github(“michael-franke/aida-package”)
library(aida)
glimpse(data_avocado)
Rows: 18,249
Columns: 7
$ Date
$ average_price
$ total_volume_sold
$ small
$ medium
$ large
$ type
data_avocado %>% arrange(Date) %>% head(.) %>% kable(.) %>% kable_styling()
Date average_price total_volume_sold small medium large type
2015-01-04 1.22 40873.28 2819.50 28287.42 49.90 conventional
2015-01-04 1.00 435021.49 364302.39 23821.16 82.15 conventional
2015-01-04 1.08 788025.06 53987.31 552906.04 39995.03 conventional
2015-01-04 1.01 80034.32 44562.12 24964.23 2752.35 conventional
2015-01-04 1.02 491738.00 7193.87 396752.18 128.82 conventional
2015-01-04 1.40 116253.44 3267.97 55693.04 109.55 conventional
Each row in the dataset contains information on the price and volume (in pounds) of avocados sold from one
outlet on a particular date for a particular type of avocado (organic or conventional). The variables in the data
set for each outlet one each date are as follows:
Variable name
Variable description
Date Date of price measurement
average_price Average price per avocado of all avocados sold
total_volume_sold Total volume of avocados sold
small Total volume of small avocados sold
medium Total volume of medium avocados sold
large Total volume of large avocados sold
type Type of avocado (organic or conventional)
b. [15 marks] Figure 1 shows three different panels examining the relationship between average price and
type of avocado.
i. [5 marks] Compare the distributions of the average prices for the conventional and organic
avocados. In particular, compare their central locations, spreads and skew to conclude whether
there is evidence in this data that the average prices of organic avocados is different from those
of conventional avocados.
Solution: The skew and spread of the two distributions are quite similar, as are the number of outlying points.
We do see that the organic avocado prices tend to be larger (note the boxplots show this the best). The
25%ile for the organic prices is larger than the 75%ile for the conventional, so we would conclude in this case
that there is a difference in central location of the prices between the two types.
ii. [5 marks] The lines in the center of the boxes in Panel (a) indicate the value of a summary statistic of
the daily outlet average prices for each of the two types of avocado in the dataset.Write a line of code
that will use the data_avocado object to compute these two values and return them in a tibble with
one column for the type and the other with the summary statistic.
data_avocado %>% group_by(type) %>%
summarize(Median = median(average_price))
conventional 1.13
organic 1.63
iii. [5 marks] Explain what was changed or added to the code to yield the different figures for (b) and panel
(c). In particular, explain why the bars look different in the two plots and why the y-axis scales of the
figures are different.
The number of bins was changed for the two plots, which increases the number of bars, decreases their width
and decreases the number of observations in each bin.
c. [20 marks] Figure 2 shows two different panels comparing how the total volume sold of conventional
avocados change over time (note that both plots are plotted on a log scale).
i. [5 marks] Which of the two panels, (a) or (b), best shows the pattern of total volume sold?
Explain your answer.
Solution: Obviously a bit subjective, but I would argue (b) best shows the pattern, because you can see hoow
the median and IQR’s change over time in a way that cannot be seen with the scatterplot.
iii. [5 marks] Would a 2D histogram make sense to use for summarizing this particular relationship? Briefly
explain why or why not.
Solution: I don’t think the 2d histogram would make that much sense here, because the dates are somewhat
discrete and regular, which we normally would not plot in a 1d histogram. However, an acceptable answer
here is that the 2d histogram makes sense in place of the scatterplot and it may help to see the trends even
better than the boxplot.
iii. [5 marks] Below is the line of code that generated the plot in panel (b). Change the line of code below
so that it produces a pair plots that contains total_volume_sold for both conventional and organic
separately over time (i.e. in different plotting areas of the same plot).
ggplot(data_avocado %>% filter(type==”conventional”),
aes(x=Date,y=total_volume_sold,group=Date)) +
geom_boxplot() + ggtitle(“Panel (b)”)+ scale_y_log10()
ggplot(data_avocado,
aes(x=Date,y=total_volume_sold,group=Date)) +
geom_boxplot() + ggtitle(“Panel (b)”)+ scale_y_log10() +
facet_grid(rows=vars(type))
iv. [5 marks] Why can’t you use the original data_avocado data object to plot the total volume sold by
the size of the avocados using the same figure you gave code to generate in part (iii) above? Explain
why and then write a line of code which would allow you to generate the necessary data object which
could then be used to make such a plot (you don’t need to include the code for the plot).
Solution: You can’t use the original object because the total volumes are in different columns and this can’t be
used with the faceting. To make them in the same column, you can use the following code:
data_avocado_long<-data_avocado %>%
pivot_longer(cols=small:large,
values_to=c(“Vol_Sold_By_Size”),
names_to=c(“Size”))
ggplot(data_avocado_long,
aes(x=Date,y=Vol_Sold_By_Size,group=Date)) +
geom_boxplot() + ggtitle(“Panel (b)”)+ scale_y_log10() +
facet_grid(rows=vars(Size))
R plots and output
Code chunk Q1
my_Costco_list <- list(
tibble(Item = c("Milk", "Coffee", "Lettuce","Pants"),
Amount = c(4,1,2,2),
Location = c("Refrigerated","Cereal","Refrigerated","Clothes"))
both_lists <- list(Costco = my_Costco_list,
IGA = tibble(
Item = c("Chicken", "Yogurt", "Pizza"),
Amount = c(2,3,1),
Location = c("Meat","Dairy","Frozen")))
Average avocado prices by type
Plots of total volume sold over time
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