咨询直方图适用性及R Studio样本均值-相对频率图绘制方法

Hey there! Let's tackle your two questions one by one—first figuring out if a histogram is a good fit for your dataset, then walking through how to build that sample mean vs relative frequency plot in R Studio.

1. 判断直方图是否适用于你的目标数据集 #

A histogram isn't a one-size-fits-all tool, so here are the key things to check:

• Data type matters most: Histograms shine with continuous numerical data (like temperature, weight, or time) or discrete data with a large range of values (like test scores 0-100). If your data is categorical (e.g., gender, brand names), skip the histogram and use a bar chart instead—they're designed for distinct groups.
• Your goal for exploration: If you want to visualize the shape of your data's distribution (is it normal? skewed? are there outliers?), a histogram is perfect. But if you're just comparing values across groups, other charts (like boxplots or grouped bar charts) might be clearer.
• Quick example: A histogram works great for "daily rainfall amounts" (continuous), but not for "count of customers per store location" (categorical locations).

2. 在R Studio中绘制样本均值（X轴）vs 相对频率（Y轴）的统计图 #

The core idea is to generate all possible samples, calculate their means, count how often each mean occurs, then plot the relative frequencies. Let's break this down for your example dataset c(1,2,3,4,5).

情况1：样本量 = 1 #

As you noted, each value is its own sample mean, so every mean has a relative frequency of 0.2. Here's how to code and plot this:

# Define the original dataset
original_data <- c(1,2,3,4,5)

# Generate all single-value samples
samples_1 <- data.frame(Sample = original_data)
samples_1$Sample_Mean <- samples_1$Sample

# Calculate relative frequencies
freq_table_1 <- table(samples_1$Sample_Mean)
rel_freq_1 <- as.data.frame(freq_table_1 / sum(freq_table_1))
colnames(rel_freq_1) <- c("Sample_Mean", "Relative_Frequency")

# Plot with ggplot2
library(ggplot2)
ggplot(rel_freq_1, aes(x = Sample_Mean, y = Relative_Frequency)) +
  geom_bar(stat = "identity", fill = "steelblue", width = 0.8) +
  labs(title = "Relative Frequency of Sample Means (Sample Size = 1)",
       x = "Sample Mean",
       y = "Relative Frequency") +
  theme_minimal()

情况2：样本量 = 2 #

We'll cover both without replacement (unique pairs only) and with replacement (allowing repeated values like (1,1)) since you mentioned "all combinations".

2.1 无放回抽样（仅唯一组合）

# Generate all unique 2-sample combinations (no replacement)
samples_2_noreplace <- combn(original_data, 2, simplify = FALSE)
# Calculate mean for each combination
means_2_noreplace <- sapply(samples_2_noreplace, mean)

# Compute relative frequencies
freq_table_2_noreplace <- table(means_2_noreplace)
rel_freq_2_noreplace <- as.data.frame(freq_table_2_noreplace / sum(freq_table_2_noreplace))
colnames(rel_freq_2_noreplace) <- c("Sample_Mean", "Relative_Frequency")

# Plot
ggplot(rel_freq_2_noreplace, aes(x = Sample_Mean, y = Relative_Frequency)) +
  geom_bar(stat = "identity", fill = "coral", width = 0.8) +
  labs(title = "Relative Frequency of Sample Means (Sample Size = 2, No Replacement)",
       x = "Sample Mean",
       y = "Relative Frequency") +
  theme_minimal()

2.2 有放回抽样（所有可能样本，含重复）

# Generate all possible 2-sample combinations (with replacement)
samples_2_replace <- expand.grid(X1 = original_data, X2 = original_data)
# Calculate mean for each sample
samples_2_replace$Sample_Mean <- rowMeans(samples_2_replace)

# Compute relative frequencies
freq_table_2_replace <- table(samples_2_replace$Sample_Mean)
rel_freq_2_replace <- as.data.frame(freq_table_2_replace / sum(freq_table_2_replace))
colnames(rel_freq_2_replace) <- c("Sample_Mean", "Relative_Frequency")

# Plot
ggplot(rel_freq_2_replace, aes(x = Sample_Mean, y = Relative_Frequency)) +
  geom_bar(stat = "identity", fill = "forestgreen", width = 0.8) +
  labs(title = "Relative Frequency of Sample Means (Sample Size = 2, With Replacement)",
       x = "Sample Mean",
       y = "Relative Frequency") +
  theme_minimal()

内容的提问来源于stack exchange，提问作者Daeyoon