R: R الإحصاء الوصفي

# 1. One line summary shows 5 key metrics
summary(scores$math)
#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#   45.0    72.0    82.0    81.5    92.0    99.0

# 2. One line skimr View the full report
library(skimr)
skim(scores$math)
# ── Variable type: numeric ──
#   min  max mean sd   p25  p50  p75  hist
#   45  99  81.5 12  72  82  92  ▇▇▇▇▇

# 3. One line dplyr Grouped Statistics
scores |> group_by(class) |> summarise(
  Average Score = mean(math),
  Median = median(math),
  Standard Deviation = sd(math),
  Highest = max(math),
  Lowest = min(math),
  Number of people = n()
)

x <- c(85, 90, 78, 92, 88)

mean(x)              # [1] 86.6
mean(x, na.rm = TRUE) # Skip NA
mean(x, trim = 0.1)   # Truncated Mean (Remove the top and bottom 10%)

median(c(85, 90, 78, 92, 88))  # [1] 88
median(c(85, 90, 78, 92, 10000))  # [1] 90  ← Not affected by 10000 Impact

# R does not have a built-in mode(), use the DescTools package
install.packages("DescTools")
library(DescTools)

Mode(c(1, 2, 2, 3, 3, 3, 4))  # [1] 3

x <- c(85, 90, 78, 92, 88)

sd(x)    # [1] 5.32  ← Standard Deviation
var(x)   # [1] 28.3  <- Variance (sd^2)

x <- c(85, 90, 78, 92, 88)

range(x)              # [1] 78 92  ← Minimum and Maximum
diff(range(x))        # [1] 14   ← Range

x <- c(85, 90, 78, 92, 88, 70, 95, 65, 88, 92)

IQR(x)                # [1] 11.5  ← Q3 - Q1
quantile(x, c(0.25, 0.5, 0.75))
#   25%   50%   75% 
# 78.25  88.0  89.75

mad(c(85, 90, 78, 92, 10000))  # Extremely Robust Discrete Measures
# [1] 4.45

x <- 1:100

# Default 0%, 25%, 50%, 75%, 100%
quantile(x)
#   0%  25%  50%  75% 100% 
#  1.0 25.75 50.5 75.25 100.0

# Custom Percentiles
quantile(x, probs = c(0.1, 0.5, 0.9))
#  10%  50%  90% 
# 10.9 50.5 90.1

x <- c(85, 90, 78, 92, 88, NA, 75, 95)

summary(x)
#    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
#   75.00   81.50   88.00   87.62   90.50   95.00       1

# Data Frame
df <- data.frame(
  age = c(20, 25, 30, 35),
  score = c(85, 90, 78, 92)
)
summary(df)
#       age            score     
#  Min.   :20.00   Min.   :78.00  
#  1st Qu.:23.75   1st Qu.:83.25  
#  Median :27.50   Median :87.50  
#  Mean   :27.50   Mean   :86.25  
#  3rd Qu.:31.25   3rd Qu.:90.50  
#  Max.   :35.00   Max.   :92.00

install.packages("skimr")
library(skimr)

x <- c(85, 90, 78, 92, 88, 70, 95, 65, 88, 92)

skim(x)
# ── Data Summary ────────────────────────
# Values                           x
# Number of rows                   10
# Number of distinct                8
# Mean                            84.2
# Standard deviation             10.13
# Min                              65
# Max                              95
# Median                          87.5
# ... (More Metrics)

library(dplyr)

# Simulation 3 Cls × 5 Student Grades
scores <- tibble(
  class = rep(c("1Cls", "2Cls", "3Cls"), each = 5),
  student = paste0("S", 1:15),
  math = c(85, 78, 92, 65, 88,    # 1 Cls
           90, 75, 80, 95, 70,    # 2 Cls
           82, 88, 76, 91, 85),   # 3 Cls
  english = c(78, 85, 88, 70, 92,
              82, 80, 90, 88, 75,
              88, 90, 78, 92, 85)
)

# Class Statistics
class_stats <- scores |>
  group_by(class) |>
  summarise(
    Number of people = n(),
    Mathematical Average = mean(math),
    Median in Mathematics = median(math),
    Mathematical Standard Deviation = sd(math),
    Top in Math = max(math),
    Lowest in Math = min(math),
    MathematicsIQR = IQR(math),
    Average English Score = mean(english)
  )

print(class_stats)
# A tibble: 3 × 9
#   class  Number of people Mathematical Average Median in Mathematics Mathematical Standard Deviation Top in Math Lowest in Math MathematicsIQR Average English Score
#   <chr> <int>    <dbl>    <dbl>      <dbl>    <dbl>    <dbl>   <dbl>    <dbl>
# 1 1Cls       5     81.6       85       11.4       92       65    17       82.6
# 2 2Cls       5     82        80        10.5       95       70    20       83
# 3 3Cls       5     84.4       85        6.02      91       76    12      86.6

# Calculate statistics for all numeric columns at once
scores |>
  group_by(class) |>
  summarise(across(where(is.numeric), list(
    mean = mean,
    sd = sd,
    median = median
  )))

# Use tapply
tapply(scores$math, scores$class, mean)
# 1Cls 2Cls 3Cls 
# 81.6 82.0 84.4

# ============================================
# 1000 Student 5 Course Comprehensive Grade Report
# Features: Complete Descriptive Statistics + Grouping + Ranking
# ============================================

library(dplyr)
library(tidyr)
library(ggplot2)

# 1. Prepare data
set.seed(42)
n <- 1000
students <- tibble(
  id = 1:n,
  class = sample(c("1Cls", "2Cls", "3Cls", "4Cls", "5Cls"), n, replace = TRUE),
  gender = sample(c("M", "F"), n, replace = TRUE),
  math = round(rnorm(n, 80, 12)),
  english = round(rnorm(n, 78, 15)),
  physics = round(rnorm(n, 75, 14)),
  chemistry = round(rnorm(n, 76, 13)),
  biology = round(rnorm(n, 80, 10))
)

cat("=== Data Volume:", nrow(students), "rows ===\n")

# 2. University-wide Comprehensive Statistics
cat("\n=== University-wide Comprehensive Statistics ===\n")
overall <- students |>
  summarise(across(c(math, english, physics, chemistry, biology),
                   list(mean = mean, sd = sd, median = median),
                   .names = "{.col}_{.fn}"))
print(overall)

# 3. Statistics by Class
cat("\n=== Math Statistics for Each Class ===\n")
class_stats <- students |>
  group_by(class) |>
  summarise(
    Number of people = n(),
    Average = round(mean(math), 2),
    Median = median(math),
    Standard Deviation = round(sd(math), 2),
    Highest = max(math),
    Lowest = min(math),
    Q1 = quantile(math, 0.25),
    Q3 = quantile(math, 0.75),
    IQR = round(IQR(math), 2)
  ) |>
  arrange(desc(Average))
print(class_stats)

# 4. Grouped by gender
cat("\n=== All genders 5 Class Average ===\n")
gender_stats <- students |>
  group_by(gender) |>
  summarise(across(c(math, english, physics, chemistry, biology),
                   mean, .names = "{.col}_Average"))
print(gender_stats)

# 5. Each Student's Total Score and Rank
cat("\n=== Top 10 Students (Total Score) ===\n")
students <- students |>
  mutate(total = math + english + physics + chemistry + biology,
         average = round(total / 5, 2))

top10 <- students |>
  arrange(desc(total)) |>
  head(10) |>
  select(id, class, gender, total, average)
print(top10)

# 6. Identify the outliers (IQR method)
cat("\n=== Students with Outliers in Math Scores ====\n")
math_q1 <- quantile(students$math, 0.25)
math_q3 <- quantile(students$math, 0.75)
math_iqr <- IQR(students$math)
lower <- math_q1 - 1.5 * math_iqr
upper <- math_q3 + 1.5 * math_iqr

outliers <- students |>
  filter(math < lower | math > upper) |>
  select(id, class, math)

cat("Normal Range:", lower, "-", upper, "\n")
cat("Number of outliers:", nrow(outliers), "\n")
print(head(outliers, 5))

# 7. Use summary() to view by subject
cat("\n=== Mathematics summary ===\n")
print(summary(students$math))

# 8. Use skimr for advanced report
library(skimr)
cat("\n=== skimr Report ===\n")
print(skim(students |> select(math, english, physics)))

# 9. Write a report
write_csv(students, "student_report.csv")
write_csv(class_stats, "class_stats.csv")
cat("\n=== The report has been generated ===\n")

=== Math Statistics for Each Class ===
# A tibble: 5 × 9
  class  Number of people Average Median Standard Deviation Highest Lowest    Q1    Q3   IQR
  <chr> <int> <dbl> <dbl>  <dbl> <int> <int> <dbl> <dbl> <dbl>
1 5Cls    201  81.0    81   12.0   114    44  72    90    18
2 1Cls    195  80.6    81   11.6   115    47  73    88    15
3 3Cls    203  79.8    80   11.8   110    49  71    88    17
4 2Cls    201  79.4    80   12.1   109    44  70    88    18
5 4Cls    200  79.1    79   12.4   116    45  70    89    19