Syllabus head (iv) — Educational measurement and evaluation | Chapter 3 of 18
67questions, every one explained
10items in the 2022 paper drew on this chapter
Why this chapter matters
Statistics is the third leg of the Measurement & Evaluation block (~30% of the paper, ~90 of 300 marks, together with Chapters 1 and 2). The 2022 paper asked direct numericals — z-scores, coefficient of variation, skewness ordering, normal-curve percentages — and definitional items on central tendency and correlation.
The good news: the exam uses only friendly numbers. Every question is designed to be solved without a calculator in under 90 seconds — if you know which formula to reach for. This chapter teaches every formula from zero.
Three questions from this chapter, solved
Every one of the 67 items is written this way — the answer, and why each wrong option is wrong.
Consider the following statements:
Statement-I: A reliability coefficient of 0.64 means the test measures true ability to the extent of 64%.
Statement-II: A validity (correlation) coefficient of 0.8 means 64% of the variance in the criterion is explained by the test.
Which one of the following is correct?
(a) Both statements are correct
(b) Statement-I is correct, but Statement-II is incorrect
(c) Statement-I is incorrect, but Statement-II is correct
(d) Both statements are incorrect
Answer (c).
Statement-I is incorrect, Statement-II is correct. "Measures true ability to the extent of" is the index of reliability, √r = √0.64 = 0.80, so the figure is 80%, not 64% — 0.64 is the proportion of true-score variance, a different statement. Statement-II is right: a correlation is squared to give the variance explained, 0.8² = 0.64 = 64%. (a) accepts Statement-I's 64%; (b) inverts both; (d) rejects the correct squaring rule.
SET A. Two sections of Class X took the same test:
Section
n
Mean
SD
A
30
40
8
B
20
50
9
Which section is MORE CONSISTENT in performance?
(a) Section A, because its SD is lower
(b) Section B, because its CV is lower
(c) Both equally consistent
(d) Cannot be determined from the data
Answer (b).
CV(A) = 8/40 = 20%; CV(B) = 9/50 = 18%. Lower CV = more consistent. Comparing raw SDs across different means (option a) is the classic error Chapter 3 Part C warns about.
Marks out of 50 are rescaled to marks out of 100 (each score doubled). Consider the following statements:
The mean is doubled.
The standard deviation remains unchanged.
Which of the statements given above is/are correct?
(a) Neither 1 nor 2
(b) 2 only
(c) Both 1 and 2
(d) 1 only
Answer (d).
1 only. Rescaling = multiplying by 2: the mean doubles AND the SD doubles. Statement 2 is the trap — SD is unchanged only under addition, not multiplication.
ORGANISING DATA
A.1 Why statistics at all?
A teacher with 60 raw scores has 60 facts and no insight. Statistics compresses them into a handful of numbers — a centre (mean), a spread (SD), a shape (skewness) — that can be compared, tracked and acted on.
Statistics used in education = descriptive statistics (describing the group you actually tested). Inferential statistics (t-tests, chi-square, ANOVA — generalising from a sample to a population) is not taught in this chapter, but the 17 July 2022 Principal paper asked two direct items on it (which test is parametric; which is not an assumption of a parametric test); it is flagged where relevant.
A.2 The frequency distribution
Raw scores are grouped into class intervals, and the number of scores falling in each interval is its frequency (f).
Class interval
Frequency
40–49
3
30–39
9
20–29
12
10–19
6
Exclusive series (10–20, 20–30…): the upper limit is excluded — a score of 20 goes into 20–30. Used for continuous data.
Inclusive series (10–19, 20–29…): both limits included. Must be converted to exact limits (9.5–19.5) before computing medians and percentiles.
Cumulative frequency (cf): running total from the bottom — "how many scored below this point." The basis of medians, quartiles, percentiles and the ogive.
A.3 Graphs — and which graph answers which question
Graph
What it is
Use it when
Histogram
Adjacent bars over class intervals; area ∝ frequency
Showing the shape of a continuous distribution
Bar diagram
Separated bars
Comparing discrete categories (streams, schools)
Frequency polygon
Midpoints of histogram tops joined by lines
Comparing two or more distributions on one chart
Ogive (cumulative frequency curve)
S-shaped curve of cf
Reading off medians, quartiles and percentiles graphically
Pie diagram
Circle cut into sectors
Parts of a whole (budget shares)
The tested pairs: ogive → percentiles; frequency polygon → comparing distributions; histogram → continuous data only (bar diagram for discrete categories).
