In-class activity #5(HW): Introduction to R for Sports Analytics, Part 2

ls()

 [1] "anova_bat_brands"           "anova_result"               "Batteries"                  "Batteries_df"              
 [5] "Batteries_temp_mat"         "Boston_df"                  "chick_aov"                  "chickwts"                  
 [9] "cor_value"                  "doubles_hit"                "firstbasestats"             "growth_df"                 
[13] "Hitters_Fixed"              "Hitters_Fixed_df"           "mean_mat_temp_combinations" "model"                     
[17] "one_way_plant_growth"       "p_values"                   "PlantGrowth"                "predicted_speed"           
[21] "reg_medv_lstat"             "sorted_p"                   "tukey_result"               "twoway_breaks_yar"         
[25] "twoway_growth"              "twoway_temp_mat"            "warpbreaks"                

doubles_hit          # prints the whole thing (only good for small datasets)

NA

#EXtract

doubles <- doubles_hit$doubles
## [1] 13.37371

class(doubles)   # should say "numeric" or "integer"

[1] "integer"

length(doubles)  # should be 100, matching your dataset

[1] 100

#Step 2: Mean, median, standard deviation

# Mean
doubles_mean <- mean(doubles)
doubles_mean

# Median
doubles_median <- median(doubles)
doubles_median

# Number of observations
doubles_n <- length(doubles)
doubles_n

# Standard deviation
doubles_sd <- sd(doubles)
doubles_sd

#Step 3: Percentage within one standard deviation

doubles_w1sd <- sum((doubles - doubles_mean)/doubles_sd < 1)/doubles_n
doubles_w1sd

[1] 0.79

## Difference from empirical rule
doubles_w1sd - 0.68

[1] 0.11

#Step 4: Percentage within two standard deviations

doubles_w2sd <- sum((doubles - doubles_mean)/doubles_sd < 2)/doubles_n
doubles_w2sd

[1] 1

## Difference from empirical rule
doubles_w2sd - 0.95

[1] 0.05

#Step 5: Percentage within three standard deviations

doubles_w3sd <- sum((doubles - doubles_mean)/doubles_sd < 3)/doubles_n
doubles_w3sd

[1] 1

## Difference from empirical rule
doubles_w3sd - 0.9973

[1] 0.0027

#Step 6: Histogram

hist(doubles, xlab = "Number of Doubles Hit", col = "green", border = "red",
     xlim = c(0,50), ylim = c(0,30), breaks = 5)

Notes on interpretation:

The distribution is roughly spread from 1 to 49 doubles, with a mean of 23.55 and median of 23.5, so it’s fairly symmetric (mean ≈ median). All 100 observations fall within two standard deviations of the mean (and three), which is why those percentages hit 100%. The one-standard-deviation figure (79%) is a bit higher than the 68% predicted by the empirical rule, which can happen with smaller or slightly non-normal datasets. The histogram shows the data isn’t perfectly bell-shaped — there’s a noticeable cluster of high values (40s) alongside the main body, suggesting a bit of right-side clustering rather than a single smooth peak.