Segmenting primary schools by achievement, teacher ratio and facilities using cluster analysis

K-Means and Hierarchical Cluster Analysis for Education and Learning

Field: Education and LearningLevel: Undergraduate thesis (S1)Method: K-Means and Hierarchical Cluster Analysis

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Grouping objects by mean assessment score, students per teacher and school facility index with K-Means and hierarchical clustering (the analysis is illustrated with synthetic data). Cluster analysis groups similar objects on several variables without class labels, using K-Means and Ward hierarchical clustering. It suits theses on segmentation or typologies of objects such as regions, customers or patients.

Segmenting primary schools by achievement, teacher ratio and facilities using cluster analysis: result sheet

Project info

Field of studyEducation and Learning
LevelUndergraduate thesis (S1)
Method typeData Exploration
Estimated build time± 3 working days
Toolsstats::kmeans, cluster::silhouette, stats::hclust, ggdendro::dendro_data, ggplot2
PriceUS$19 - US$122

Research goal

Grouping objects by mean assessment score, students per teacher and school facility index with K-Means and hierarchical clustering (the analysis is illustrated with synthetic data).

Variables

Role	Variable	Unit
Main	Mean assessment score	score
Supporting 1	Students per teacher	ratio
Supporting 2	School facility index	index

Example result

4Optimal k (silhouette)
0.638Mean silhouette
0.876Between SS / total SS
1ARI K-Means vs Ward
24Smallest cluster (n)

The highest mean silhouette (0.638) occurs at k = 4, and K-Means explains 87.6% of total variation (BSS/TSS). Ward hierarchical clustering agrees closely with K-Means (ARI = 1.000). Cluster C4 has the highest mean Mean assessment score (91.51) across 27 objects.

Computed from illustrative synthetic data, not from a real study.

About K-Means and Hierarchical Cluster Analysis

Cluster analysis groups similar objects on several variables without class labels, using K-Means and Ward hierarchical clustering. It suits theses on segmentation or typologies of objects such as regions, customers or patients.

Steps

1Choose the clustering variables and standardise them (z-scores)
2Compute WSS (elbow) and mean silhouette for k = 2 to 8
3Set k by the highest silhouette and run kmeans (nstart = 25)
4Run hierarchical clustering with hclust ward.D2 and cut at the same k
5Measure agreement between K-Means and Ward with the adjusted Rand index
6Build mean profiles per cluster and show them on the first two principal components

Assumptions to check

Variables are on comparable scales after standardisation
Clusters are roughly spherical with similar spread (K-Means)
No extreme outliers dominate the distances
Variables are not highly redundant with one another

Reading and reporting the results

Report the chosen k with its mean silhouette and BSS/TSS ratio, then the agreement with hierarchical clustering (ARI). Name each cluster from its z-score or raw mean profile and describe the main differences.

Example R code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

Show code

# Contoh kode R: K-Means and Hierarchical Cluster Analysis
suppressPackageStartupMessages({
  library(ggplot2)
  library(patchwork)
  library(cluster)
  library(ggdendro)
})
set.seed(42)
# ---- Gaya grafik ----
pal <- c("#1f6feb", "#e8590c", "#2f9e44", "#ae3ec9", "#f59f00")
warna <- list(bg = "#f4f6fa", panel = "#ffffff", teks = "#1f2933", redup = "#5f6b78", grid = "#e3e8ee", bar = "#1d3557")
tata <- 1
theme_set(theme_minimal(base_size = 11) + theme(legend.position = "bottom"))

# ---- Data sintetis: objek dari 3 atau 4 kelompok laten, 4 variabel karakteristik ----
n <- 200
positif <- function(x, m) if (m > 0) pmax(x, 0.05 * m) else x   # cegah nilai negatif yang tidak wajar
k_benar <- sample(3:4, 1)
repeat {                                       # pusat kelompok yang cukup terpisah (skala z)
  pusat <- matrix(rnorm(k_benar * 4, 0, 1.6), k_benar, 4)
  if (min(dist(pusat)) > 3.2) break
}
anggota <- sample(seq_len(k_benar), n, replace = TRUE, prob = runif(k_benar, 0.6, 1.4))
sebaran <- runif(1, 0.5, 0.72)
z <- pusat[anggota, ] + matrix(rnorm(n * 4, 0, sebaran), n, 4)
d <- data.frame(mean_assessment_score = positif(100 + 0.6 * 15 * z[, 1], 100),
                students_per_teacher = positif(50 + 0.6 * 10 * z[, 2], 50),
                school_facility_index = positif(30 + 0.6 * 6 * z[, 3], 30),
                x3 = round(50 + 6 * z[, 4], 2))
write.csv(d, "data_contoh.csv", row.names = FALSE)

# ---- Standarisasi variabel ----
vars <- c("mean_assessment_score", "students_per_teacher", "school_facility_index", "x3")
xs <- scale(d[vars])
jarak <- dist(xs)

# ---- Penentuan jumlah klaster: elbow (WSS) dan silhouette rata-rata, k = 2..8 ----
daftar_k <- 2:8
uji_k <- lapply(daftar_k, function(k) {
  km <- kmeans(xs, centers = k, nstart = 25, iter.max = 50)
  sil <- cluster::silhouette(km$cluster, jarak)
  c(k = k, wss = km$tot.withinss, sil = mean(sil[, "sil_width"]))
})
uji_k <- as.data.frame(do.call(rbind, uji_k))
print(round(uji_k, 3))
k_best <- uji_k$k[which.max(uji_k$sil)]
cat("Jumlah klaster terpilih (silhouette maksimum):", k_best, "\n")

# ---- K-Means akhir (nstart 25); label klaster diurutkan menurut rerata Y ----
km <- kmeans(xs, centers = k_best, nstart = 25, iter.max = 50)
urut <- order(tapply(d$mean_assessment_score, km$cluster, mean))
d$klaster <- factor(paste0("C", match(km$cluster, urut)), levels = paste0("C", seq_len(k_best)))
sil_akhir <- mean(cluster::silhouette(km$cluster, jarak)[, "sil_width"])
rasio_bss <- km$betweenss / km$totss

# ---- Klaster hierarki Ward (ward.D2) dan kesesuaiannya dengan K-Means ----
hc <- hclust(jarak, method = "ward.D2")
ward <- cutree(hc, k = k_best)
print(table(KMeans = d$klaster, Ward = ward))
ari <- function(a, b) {
  # adjusted Rand index (Hubert dan Arabie)
  tb <- table(a, b); c2 <- function(x) sum(x * (x - 1) / 2)
  s_ij <- c2(tb); s_a <- c2(rowSums(tb)); s_b <- c2(colSums(tb)); tot <- c2(sum(tb))
  harap <- s_a * s_b / tot
  (s_ij - harap) / (0.5 * (s_a + s_b) - harap)
}
ari_km_ward <- ari(d$klaster, ward)
cat(sprintf("Adjusted Rand index K-Means vs Ward = %.3f\n", ari_km_ward))

# ---- Profil klaster (rerata satuan asli) ----
profil <- aggregate(d[vars], by = list(klaster = d$klaster), FUN = mean)
profil$n <- as.numeric(table(d$klaster))
print(profil, digits = 4)
k_atas <- as.character(profil$klaster[which.max(profil$mean_assessment_score)])


# ---- Grafik ----
dk <- rbind(data.frame(k = uji_k$k, nilai = uji_k$sil, ukuran = "Mean silhouette"),
            data.frame(k = uji_k$k, nilai = uji_k$wss, ukuran = "Within SS (elbow)"))
p1 <- ggplot(dk, aes(k, nilai)) +
  geom_vline(xintercept = k_best, linetype = "dashed", colour = warna$redup) +
  geom_line(colour = pal[1], linewidth = 0.9) +
  geom_point(aes(colour = k == k_best), size = 2.2) +
  scale_colour_manual(values = c(`FALSE` = pal[1], `TRUE` = pal[2]), guide = "none") +
  facet_wrap(~ukuran, ncol = 1, scales = "free_y") +
  scale_x_continuous(breaks = daftar_k) +
  labs(title = "Choosing k", x = "Number of clusters k", y = NULL)
pc <- prcomp(xs)
ve <- 100 * pc$sdev^2 / sum(pc$sdev^2)
sk <- data.frame(PC1 = pc$x[, 1], PC2 = pc$x[, 2], klaster = d$klaster)
pusat_pc <- aggregate(cbind(PC1, PC2) ~ klaster, data = sk, FUN = mean)
p2 <- ggplot(sk, aes(PC1, PC2, colour = klaster)) +
  stat_ellipse(aes(fill = klaster), geom = "polygon", alpha = 0.12, level = 0.9, show.legend = FALSE) +
  geom_point(size = 1.5, alpha = 0.75) +
  geom_point(data = pusat_pc, shape = 4, size = 4, stroke = 1.4, colour = warna$teks) +
  geom_text(data = pusat_pc, aes(label = klaster), colour = warna$teks, fontface = "bold", size = 3.6, vjust = -1.1) +
  scale_colour_manual(values = pal, name = "Cluster") +
  scale_fill_manual(values = pal) +
  labs(title = "K-Means clusters on the first two PCs", x = sprintf("PC1 (%.1f%%)", ve[1]), y = sprintf("PC2 (%.1f%%)", ve[2]))
zp <- aggregate(as.data.frame(xs), by = list(klaster = d$klaster), FUN = mean)
nama_var <- sapply(c("mean_assessment_score", "students_per_teacher", "school_facility_index", "x3 (extra)"), function(s) paste(strwrap(s, 14), collapse = "
"))
pl <- data.frame(klaster = rep(zp$klaster, length(vars)), variabel = rep(nama_var, each = nrow(zp)), z = unlist(zp[vars]))
pl$variabel <- factor(pl$variabel, levels = unique(nama_var))
p3 <- ggplot(pl, aes(variabel, klaster, fill = z)) +
  geom_tile(colour = warna$panel, linewidth = 0.8) +
  geom_text(aes(label = sprintf("%.2f", round(z, 2) + 0)), colour = warna$teks, size = 3.1) +
  scale_fill_gradient2(low = pal[1], mid = warna$panel, high = pal[2], midpoint = 0, name = "z") +
  labs(title = "Cluster profile (mean z-score)", x = NULL, y = NULL) +
  theme(panel.grid = element_blank(), legend.position = "none", axis.text.x = element_text(size = rel(0.8)))
dd <- ggdendro::dendro_data(as.dendrogram(hc), type = "rectangle")
h_tinggi <- sort(hc$height, decreasing = TRUE)
h_potong <- mean(h_tinggi[(k_best - 1):k_best])
p4 <- ggplot(ggdendro::segment(dd)) +
  geom_segment(aes(x = x, y = y, xend = xend, yend = yend), colour = pal[3], linewidth = 0.35) +
  geom_hline(yintercept = h_potong, linetype = "dashed", colour = pal[2], linewidth = 0.8) +
  annotate("text", x = nrow(d) * 0.98, y = h_potong, label = sprintf("cut: k = %d", k_best), hjust = 1, vjust = -0.5,
           colour = warna$teks, size = 3) +
  labs(title = "Ward (ward.D2) dendrogram", x = "Objects", y = "Height") +
  theme(axis.text.x = element_blank(), panel.grid.major.x = element_blank())
p_hasil <- if (tata == 1) ((p2 | p1) / (p4 | p3)) + plot_layout(widths = c(1.5, 1), heights = c(1.3, 1)) else
  ((p2 / p4) | (p1 / p3)) + plot_layout(widths = c(1.5, 1))

print(p_hasil)

The project file you can download

The original project file is available. It is not just the picture above: you get the working R project. It can be downloaded after payment, and we send it by WhatsApp or email.

ZIP: analisis.R + data_contoh.csv + BACA-DULU.txt

What is inside the ZIP

The complete analysis script (analisis.R), commented step by step, ready to run in RStudio.
A sample dataset (data_contoh.csv) so the script runs straight away.
A short guide (BACA-DULU.txt): which packages to install, how to run it and how to swap in your own data.

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

Package 1

Code and Explanation

US$19

excl. 11% VAT

Duration: 3 working days

Output: R files + result figures

Deliverables

Fully commented R code (.R) for K-Means and Hierarchical Cluster Analysis
Example data and step-by-step run instructions
Ready-to-use result figures and metrics table
Short explanation of the method, its assumptions and how to read the results

Choose Package 1

Package 2 · most chosen

Your Data Analysis + Interpretation

US$56

excl. 11% VAT

Duration: 7 working days

Output: Code + analysis + interpretation notes

Includes all of Package 1, plus

Adapting the code to your own research dataset (CSV or Excel)
Assumption checks, result validation and data cleaning
Tables and figures formatted for your manuscript
Interpretation notes for the methods and discussion sections, for you to write up in your own words

Choose Package 2

Package 3

Full Guidance

US$122

excl. 11% VAT

Duration: 12-15 working days

Output: Code + analysis + guidance until ready to present

Includes all of Packages 1 & 2, plus

Comparison against one alternative method with the reasoning for the choice
Two 60-minute online coaching sessions so you fully understand the code and results
Revisions following your supervisor feedback (up to 3 rounds)
Practice Q&A to prepare for your seminar and defence
Full documentation (README, R package list (sessionInfo)) so the results can be reproduced

Choose Package 3

Payment: 50% down payment before work starts, balance after the deliverables are handed over
Tax: Prices exclude 11% VAT
Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions

Do I get the real project file?

Yes. The original project file is a ZIP containing the complete analisis.R script, a data_contoh.csv sample dataset and a BACA-DULU.txt guide. It can be downloaded after payment, and we send it by WhatsApp or email. For your own data (Package 2 and 3) the script is adapted to your dataset.

Is this suitable for a Undergraduate thesis (S1)?

Yes. K-Means and Hierarchical Cluster Analysis is commonly used at this level in Education and Learning. We adapt the analysis to your research question, your own data and your supervisor's requirements.

Is the result sheet real data?

No. The sheet is computed from illustrative synthetic data so you can see the kind of output R Studio gives. For your order we run the same method on your own data.

Will I understand the code?

That is the point of the packages. Every script is commented, and Package 3 includes two coaching sessions plus practice questions so you can explain the method and the results at your seminar and defence.

How is the price decided?

Each project has three packages: Package 1 (code and explanation) US$19, Package 2 (your data analysis and interpretation) US$56 and Package 3 (full guidance) US$122, excluding 11% VAT. Larger datasets, extra methods or tight deadlines adjust the quote after a short consultation.

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