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+ggplot(diamonds, aes(x = carat)) + + geom_histogram(binwidth = 0.5) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-2-1.png) + +# Typical Values + +``` r +smaller <- diamonds |> + filter(carat < 3) + +ggplot(smaller, aes(x = carat)) + + geom_histogram(binwidth = 0.01) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-3-1.png) + +# Unusual Values + +``` r +ggplot(diamonds, aes(x = y)) + + geom_histogram(binwidth = 0.5) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-4-1.png) + +``` r +ggplot(diamonds, aes(x = y)) + + geom_histogram(binwidth = 0.5) + + coord_cartesian(ylim = c(0, 50)) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-5-1.png) + +coord_cartesian() also has an xlim() argument for when you need to zoom +into the x-axis. ggplot2 also has xlim() and ylim() functions that work +slightly differently: they throw away the data outside the limits. + +``` r +unusual <- diamonds |> + filter(y < 3 | y > 20) |> + select(price, x, y, z) |> + arrange(y) +unusual +``` + + # A tibble: 9 × 4 + price x y z + + 1 5139 0 0 0 + 2 6381 0 0 0 + 3 12800 0 0 0 + 4 15686 0 0 0 + 5 18034 0 0 0 + 6 2130 0 0 0 + 7 2130 0 0 0 + 8 2075 5.15 31.8 5.12 + 9 12210 8.09 58.9 8.06 + +# Exercises pt 1 of 5 + +1. x (length), y (width), z(depth) + +``` r +ggplot(diamonds, aes(x = z)) + + geom_histogram(binwidth = 0.1) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-7-1.png) + +The x and y measurements have similar distibutions while the z variable +is skewed towards smaller depth values. The length and width values are +larger than the depth which aligns with the shape of a diamond. + +2. + +``` r +ggplot(diamonds, aes(x = price)) + + geom_histogram(binwidth = 500) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-8-1.png) + +``` r +ggplot(diamonds, aes(x = price)) + + geom_histogram(binwidth = 50) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-9-1.png) + +The majority of diamonds are found in the lower price range creating a +skew to the right towards higher values. + +3. + +``` r +diamonds %>% + count(carat) %>% + filter(carat == 0.99 | carat == 1.00) +``` + + # A tibble: 2 × 2 + carat n + + 1 0.99 23 + 2 1 1558 + +There are more 1 carat diamonds because whole carats are a standard in +diamond advertising? + +4. coord_cartesian() adjusts the view without removing data, + maintaining the same bin counts x and ylin() filter out data outside + the set range which can alter the shape of your histogram. If + binwidth is not set, a defeault is selected which may not display + the desired patterns. Zooming to half a bar with xlim() may exclude + bins and break the visual. + +# Unusual Values + +You can use the if_else() function to replace unusual values with NA: + +``` r +diamonds2 <- diamonds |> + mutate(y = if_else(y < 3 | y > 20, NA, y)) + +ggplot(diamonds2, aes(x = x, y = y)) + + geom_point() +``` + + Warning: Removed 9 rows containing missing values or values outside the scale range + (`geom_point()`). + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-11-1.png) + +``` r +ggplot(diamonds2, aes(x = x, y = y)) + + geom_point(na.rm = TRUE) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-12-1.png) + +``` r +nycflights13::flights |> + mutate( + cancelled = is.na(dep_time), + sched_hour = sched_dep_time %/% 100, + sched_min = sched_dep_time %% 100, + sched_dep_time = sched_hour + (sched_min / 60) + ) |> + ggplot(aes(x = sched_dep_time)) + + geom_freqpoly(aes(color = cancelled), binwidth = 1/4) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-13-1.png) + +# Exercises pt 2 of 5 + +1. Histograms contain continous quantitative data and will exclude + missing values from the plot while bar charts display categorical + data meaning they can display missing data as “NA” or “missing” . +2. This function removes any missing values marked as NA +3. + +``` r +library(nycflights13) + +flights |> + mutate( + cancelled = is.na(dep_time), + sched_hour = sched_dep_time %/% 100, + sched_min = sched_dep_time %% 100, + sched_dep_time = sched_hour + (sched_min / 60) + ) |> + ggplot(aes(x = sched_dep_time)) + + geom_freqpoly(aes(color = cancelled), binwidth = 1/4) + + facet_wrap(~cancelled, scales = "free_y") + # Try "free_y", "free", or "fixed" + labs( + x = "Scheduled Departure Time (Hour)", + y = "Number of Flights", + color = "Cancelled" + ) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-14-1.png) + +# A Categorical and Numerical Variable + +``` r +ggplot(diamonds, aes(x = price)) + + geom_freqpoly(aes(color = cut), binwidth = 500, linewidth = 0.75) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-15-1.png) + +``` r +ggplot(diamonds, aes(x = price, y = after_stat(density))) + + geom_freqpoly(aes(color = cut), binwidth = 500, linewidth = 0.75) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-16-1.png) + +``` r +ggplot(diamonds, aes(x = cut, y = price)) + + geom_boxplot() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-17-1.png) + +``` r +ggplot(mpg, aes(x = class, y = hwy)) + + geom_boxplot() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-18-1.png) + +we can reorder class based on the median value of hwy: + +``` r +ggplot(mpg, aes(x = fct_reorder(class, hwy, median), y = hwy)) + + geom_boxplot() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-19-1.png) + +``` r +ggplot(mpg, aes(x = hwy, y = fct_reorder(class, hwy, median))) + + geom_boxplot() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-20-1.png) + +# Exercises pt 3 of 5 + +1. + +``` r +flights |> + mutate( + sched_dep_time = sched_dep_time %/% 100 + (sched_dep_time %% 100) / 60, + cancelled = is.na(dep_time) + ) |> + ggplot(aes(x = sched_dep_time, y = fct_reorder(factor(cancelled), sched_dep_time, median))) + + geom_boxplot() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-21-1.png) + +2. The carat of a diamond offers a good positive correlation with price + making it a good predictor of price. + +``` r +ggplot(diamonds, aes(x = carat, y = price)) + + geom_point(alpha = 0.1) + + geom_smooth(method = lm) +``` + + `geom_smooth()` using formula = 'y ~ x' + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-22-1.png) + +``` r +ggplot(diamonds, aes(x = carat, y = cut)) + + geom_boxplot() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-23-1.png) + +There is a negative correlation between carat and cut meaning a higher +carat is not equal to a better quality diamond. 3. + +``` r +ggplot(diamonds, aes(x = carat, y = cut)) + + geom_boxplot() + + coord_flip() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-24-1.png) + +This version makes the trend between cut and carat more visible. 4. + +``` r +library(lvplot) +ggplot(diamonds, aes(x = cut, y = price)) + + geom_lv() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-25-1.png) + +A small number of diamonds are extremely expensiv but ideal and premuim +cuts have more consistent pricing. 5. + +``` r +ggplot(diamonds, aes(x = cut, y = price)) + + geom_violin() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-26-1.png) + +``` r +ggplot(diamonds, aes(x = price)) + + geom_histogram(binwidth = 500) + + facet_wrap(~ cut) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-26-2.png) + +``` r +ggplot(diamonds, aes(x = price, color = cut)) + + geom_freqpoly(binwidth = 500) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-26-3.png) + +``` r +ggplot(diamonds, aes(x = price, color = cut)) + + geom_density() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-26-4.png) + +The violin plot is good for easy comparisons between distribution shapes +but doesn’t display the count The histogram shows the number of diamonds +(count) but is not great for easy comparison of trends The frequency +polygon has all lines on one plot making for an easier comparision but +there is some overlap which can disrupt interpretation The density plot +show distribution shape clearly but doesn’t display the counts. + +6. geom_beeswarm() Arranges points side-by-side in a compact, + non-overlapping layout. geom_quasirandom() Adds jitter using + structured patterns + +# Two Categorical Variables + +``` r +ggplot(diamonds, aes(x = cut, y = color)) + + geom_count() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-27-1.png) + +The size of each circle in the plot displays how many observations +occurred at each combination of values. + +``` r +diamonds |> + count(color, cut) |> + ggplot(aes(x = color, y = cut)) + + geom_tile(aes(fill = n)) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-28-1.png) + +# Exercises pt 4 of 5 + +1. + +``` r +diamonds |> + count(color, cut) |> + group_by(color) |> + mutate(prop_within_color = n / sum(n)) |> + ggplot(aes(x = color, y = cut)) + + geom_tile(aes(fill = prop_within_color)) + + scale_fill_gradient(low = "white", high = "steelblue") +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-29-1.png) + +2. + +``` r +segment_counts <- diamonds |> + count(color, cut) |> + arrange(color, desc(n)) + +segment_counts +``` + + # A tibble: 35 × 3 + color cut n + + 1 D Ideal 2834 + 2 D Premium 1603 + 3 D Very Good 1513 + 4 D Good 662 + 5 D Fair 163 + 6 E Ideal 3903 + 7 E Very Good 2400 + 8 E Premium 2337 + 9 E Good 933 + 10 E Fair 224 + # ℹ 25 more rows + +``` r +diamonds |> + ggplot(aes(x = color, fill = cut)) + + geom_bar(position = "fill") +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-30-1.png) + +You can see how common each cut is between colors and the distribution +of cuts across colors. 3. + +``` r +flights |> + group_by(dest, month) |> + summarise(avg_delay = mean(dep_delay, na.rm = TRUE), .groups = "drop") |> + ggplot(aes(x = factor(month), y = dest, fill = avg_delay)) + + geom_tile(color = "white") + + scale_fill_gradient(low = "lightyellow", high = "firebrick", na.value = "grey90") + + labs( + x = "Month", + y = "Destination", + fill = "Avg Delay (min)" + ) + + theme_minimal(base_size = 13) + + theme(axis.text.y = element_text(size = 6)) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-31-1.png) + +There are too many destinations which then overlap making it hard to +read. Filtering to specific destinations or airlines could improve the +readability. + +# Two Numerical Variables + +``` r +ggplot(smaller, aes(x = carat, y = price)) + + geom_point() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-32-1.png) + +``` r +ggplot(smaller, aes(x = carat, y = price)) + + geom_point(alpha = 1 / 100) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-33-1.png) + +``` r +ggplot(smaller, aes(x = carat, y = price)) + + geom_bin2d() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-34-1.png) + +``` r +# install.packages("hexbin") +ggplot(smaller, aes(x = carat, y = price)) + + geom_hex() +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-34-2.png) + +``` r +ggplot(smaller, aes(x = carat, y = price)) + + geom_boxplot(aes(group = cut_width(carat, 0.1))) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-35-1.png) + +# Exercises pt 5 of 5 + +1. + +``` r +ggplot(diamonds, aes(x = price, color = cut_width(carat, 0.25))) + + geom_freqpoly(binwidth = 500) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-36-1.png) + +``` r +ggplot(diamonds, aes(x = price, color = cut_number(carat, 5))) + + geom_freqpoly(binwidth = 500) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-36-2.png) + +cut_width() shows how price varies across fixed carat ranges +cut_number() allows has less overlap in the cut range 2. + +``` r +ggplot(diamonds, aes(x = carat, color = cut_width(price, width = 2000))) + + geom_freqpoly(binwidth = 0.1) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-37-1.png) + +3. + +``` r +diamonds |> + mutate(size_group = case_when( + percent_rank(carat) < 0.025 ~ "Small", + percent_rank(carat) > 0.975 ~ "Large", + TRUE ~ NA_character_ + )) |> + filter(!is.na(size_group)) |> + ggplot(aes(x = price, fill = size_group)) + + geom_density(alpha = 0.6) + + facet_wrap(~size_group) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-38-1.png) + +The price of larger diamonds is broad with some small outliers while the +price of small diamonds is peaked at lower prices. 4. + +``` r +ggplot(diamonds, aes(x = carat, y = price, color = cut)) + + geom_point(alpha = 0.4, size = 1) +``` + +![](Chapter_10_files/figure-commonmark/unnamed-chunk-39-1.png) + +5. A scatterplot can detect joint outliers or unsual combinations +6. Advantages: prevents overcrowding in dense regions and balances + sample sizes per bin Disadvantages: the bins widths are uneven which + makes the x axis hard to read diff --git a/Chapter_10.qmd b/Chapter_10.qmd new file mode 100644 index 0000000..2c01c31 --- /dev/null +++ b/Chapter_10.qmd @@ -0,0 +1,345 @@ +--- +title: "Chapter 10, Exploratory Data Analysis" +format: gfm +--- + +```{r} +library(tidyverse) +``` + +# Variation +```{r} +ggplot(diamonds, aes(x = carat)) + + geom_histogram(binwidth = 0.5) +``` + +# Typical Values +```{r} +smaller <- diamonds |> + filter(carat < 3) + +ggplot(smaller, aes(x = carat)) + + geom_histogram(binwidth = 0.01) +``` +# Unusual Values + +```{r} +ggplot(diamonds, aes(x = y)) + + geom_histogram(binwidth = 0.5) +``` + +```{r} +ggplot(diamonds, aes(x = y)) + + geom_histogram(binwidth = 0.5) + + coord_cartesian(ylim = c(0, 50)) +``` +coord_cartesian() also has an xlim() argument for when you need to zoom into the x-axis. ggplot2 also has xlim() and ylim() functions that work slightly differently: they throw away the data outside the limits. + +```{r} +unusual <- diamonds |> + filter(y < 3 | y > 20) |> + select(price, x, y, z) |> + arrange(y) +unusual +``` + +# Exercises pt 1 of 5 +1. x (length), y (width), z(depth) +```{r} +ggplot(diamonds, aes(x = z)) + + geom_histogram(binwidth = 0.1) +``` +The x and y measurements have similar distibutions while the z variable is skewed towards smaller depth values. The length and width values are larger than the depth which aligns with the shape of a diamond. + +2. +```{r} +ggplot(diamonds, aes(x = price)) + + geom_histogram(binwidth = 500) +``` + +```{r} +ggplot(diamonds, aes(x = price)) + + geom_histogram(binwidth = 50) +``` + +The majority of diamonds are found in the lower price range creating a skew to the right towards higher values. + +3. +```{r} +diamonds %>% + count(carat) %>% + filter(carat == 0.99 | carat == 1.00) +``` +There are more 1 carat diamonds because whole carats are a standard in diamond advertising? + +4. coord_cartesian() adjusts the view without removing data, maintaining the same bin counts +x and ylin() filter out data outside the set range which can alter the shape of your histogram. If binwidth is not set, a defeault is selected which may not display the desired patterns. Zooming to half a bar with xlim() may exclude bins and break the visual. + +# Unusual Values +You can use the if_else() function to replace unusual values with NA: +```{r} +diamonds2 <- diamonds |> + mutate(y = if_else(y < 3 | y > 20, NA, y)) + +ggplot(diamonds2, aes(x = x, y = y)) + + geom_point() +``` + +```{r} +ggplot(diamonds2, aes(x = x, y = y)) + + geom_point(na.rm = TRUE) +``` + +```{r} +nycflights13::flights |> + mutate( + cancelled = is.na(dep_time), + sched_hour = sched_dep_time %/% 100, + sched_min = sched_dep_time %% 100, + sched_dep_time = sched_hour + (sched_min / 60) + ) |> + ggplot(aes(x = sched_dep_time)) + + geom_freqpoly(aes(color = cancelled), binwidth = 1/4) +``` + +# Exercises pt 2 of 5 +1. Histograms contain continous quantitative data and will exclude missing values from the plot while bar charts display categorical data meaning they can display missing data as "NA" or "missing" . +2. This function removes any missing values marked as NA +3. +```{r} +library(nycflights13) + +flights |> + mutate( + cancelled = is.na(dep_time), + sched_hour = sched_dep_time %/% 100, + sched_min = sched_dep_time %% 100, + sched_dep_time = sched_hour + (sched_min / 60) + ) |> + ggplot(aes(x = sched_dep_time)) + + geom_freqpoly(aes(color = cancelled), binwidth = 1/4) + + facet_wrap(~cancelled, scales = "free_y") + # Try "free_y", "free", or "fixed" + labs( + x = "Scheduled Departure Time (Hour)", + y = "Number of Flights", + color = "Cancelled" + ) +``` + +# A Categorical and Numerical Variable +```{r} +ggplot(diamonds, aes(x = price)) + + geom_freqpoly(aes(color = cut), binwidth = 500, linewidth = 0.75) +``` + +```{r} +ggplot(diamonds, aes(x = price, y = after_stat(density))) + + geom_freqpoly(aes(color = cut), binwidth = 500, linewidth = 0.75) +``` + +```{r} +ggplot(diamonds, aes(x = cut, y = price)) + + geom_boxplot() +``` + +```{r} +ggplot(mpg, aes(x = class, y = hwy)) + + geom_boxplot() +``` +we can reorder class based on the median value of hwy: +```{r} +ggplot(mpg, aes(x = fct_reorder(class, hwy, median), y = hwy)) + + geom_boxplot() +``` + +```{r} +ggplot(mpg, aes(x = hwy, y = fct_reorder(class, hwy, median))) + + geom_boxplot() +``` + +# Exercises pt 3 of 5 +1. +```{r} +flights |> + mutate( + sched_dep_time = sched_dep_time %/% 100 + (sched_dep_time %% 100) / 60, + cancelled = is.na(dep_time) + ) |> + ggplot(aes(x = sched_dep_time, y = fct_reorder(factor(cancelled), sched_dep_time, median))) + + geom_boxplot() +``` +2. The carat of a diamond offers a good positive correlation with price making it a good predictor of price. +```{r} +ggplot(diamonds, aes(x = carat, y = price)) + + geom_point(alpha = 0.1) + + geom_smooth(method = lm) +``` + +```{r} +ggplot(diamonds, aes(x = carat, y = cut)) + + geom_boxplot() +``` +There is a negative correlation between carat and cut meaning a higher carat is not equal to a better quality diamond. +3. +```{r} +ggplot(diamonds, aes(x = carat, y = cut)) + + geom_boxplot() + + coord_flip() +``` +This version makes the trend between cut and carat more visible. +4. +```{r} +library(lvplot) +ggplot(diamonds, aes(x = cut, y = price)) + + geom_lv() +``` +A small number of diamonds are extremely expensiv but ideal and premuim cuts have more consistent pricing. +5. +```{r} +ggplot(diamonds, aes(x = cut, y = price)) + + geom_violin() + +ggplot(diamonds, aes(x = price)) + + geom_histogram(binwidth = 500) + + facet_wrap(~ cut) + +ggplot(diamonds, aes(x = price, color = cut)) + + geom_freqpoly(binwidth = 500) + +ggplot(diamonds, aes(x = price, color = cut)) + + geom_density() + +``` +The violin plot is good for easy comparisons between distribution shapes but doesn't display the count +The histogram shows the number of diamonds (count) but is not great for easy comparison of trends +The frequency polygon has all lines on one plot making for an easier comparision but there is some overlap which can disrupt interpretation +The density plot show distribution shape clearly but doesn't display the counts. + +6. +geom_beeswarm() Arranges points side-by-side in a compact, non-overlapping layout. +geom_quasirandom() Adds jitter using structured patterns + +# Two Categorical Variables + +```{r} +ggplot(diamonds, aes(x = cut, y = color)) + + geom_count() +``` +The size of each circle in the plot displays how many observations occurred at each combination of values. + +```{r} +diamonds |> + count(color, cut) |> + ggplot(aes(x = color, y = cut)) + + geom_tile(aes(fill = n)) +``` +# Exercises pt 4 of 5 +1. +```{r} +diamonds |> + count(color, cut) |> + group_by(color) |> + mutate(prop_within_color = n / sum(n)) |> + ggplot(aes(x = color, y = cut)) + + geom_tile(aes(fill = prop_within_color)) + + scale_fill_gradient(low = "white", high = "steelblue") +``` +2. +```{r} + +segment_counts <- diamonds |> + count(color, cut) |> + arrange(color, desc(n)) + +segment_counts + +diamonds |> + ggplot(aes(x = color, fill = cut)) + + geom_bar(position = "fill") + +``` +You can see how common each cut is between colors and the distribution of cuts across colors. +3. +```{r} +flights |> + group_by(dest, month) |> + summarise(avg_delay = mean(dep_delay, na.rm = TRUE), .groups = "drop") |> + ggplot(aes(x = factor(month), y = dest, fill = avg_delay)) + + geom_tile(color = "white") + + scale_fill_gradient(low = "lightyellow", high = "firebrick", na.value = "grey90") + + labs( + x = "Month", + y = "Destination", + fill = "Avg Delay (min)" + ) + + theme_minimal(base_size = 13) + + theme(axis.text.y = element_text(size = 6)) +``` +There are too many destinations which then overlap making it hard to read. Filtering to specific destinations or airlines could improve the readability. + +# Two Numerical Variables +```{r} +ggplot(smaller, aes(x = carat, y = price)) + + geom_point() +``` + +```{r} +ggplot(smaller, aes(x = carat, y = price)) + + geom_point(alpha = 1 / 100) +``` + +```{r} +ggplot(smaller, aes(x = carat, y = price)) + + geom_bin2d() + +# install.packages("hexbin") +ggplot(smaller, aes(x = carat, y = price)) + + geom_hex() +``` + +```{r} +ggplot(smaller, aes(x = carat, y = price)) + + geom_boxplot(aes(group = cut_width(carat, 0.1))) +``` +# Exercises pt 5 of 5 +1. +```{r} +ggplot(diamonds, aes(x = price, color = cut_width(carat, 0.25))) + + geom_freqpoly(binwidth = 500) + +ggplot(diamonds, aes(x = price, color = cut_number(carat, 5))) + + geom_freqpoly(binwidth = 500) + +``` +cut_width() shows how price varies across fixed carat ranges +cut_number() allows has less overlap in the cut range +2. +```{r} +ggplot(diamonds, aes(x = carat, color = cut_width(price, width = 2000))) + + geom_freqpoly(binwidth = 0.1) +``` + +3. +```{r} +diamonds |> + mutate(size_group = case_when( + percent_rank(carat) < 0.025 ~ "Small", + percent_rank(carat) > 0.975 ~ "Large", + TRUE ~ NA_character_ + )) |> + filter(!is.na(size_group)) |> + ggplot(aes(x = price, fill = size_group)) + + geom_density(alpha = 0.6) + + facet_wrap(~size_group) +``` +The price of larger diamonds is broad with some small outliers while the price of small diamonds is peaked at lower prices. +4. +```{r} +ggplot(diamonds, aes(x = carat, y = price, color = cut)) + + geom_point(alpha = 0.4, size = 1) + +``` +5. 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