ICAR AIEEA-PG Biometry, Statistics & Computing for Forestry: practice questions

ICAR AIEEA-PG — Forestry/Agroforestry & Silviculture (Major Subject Group 09) · India · National Testing Agency for ICAR

Original practice questions written to the published syllabus · not past papers

10worked here, free

60written to this exam in this subject

10syllabus units

What this subject covers

The statistics and computing used in forest inventory, experiments and modelling, from descriptive statistics and sampling to regression, designed experiments and scripting. Econometrics and business statistics are taught in the Agribusiness track, and sampling theory and spatial statistics in full in the Agricultural Statistics track; they are not repeated.

In the exams: ICAR AIEEA-PG Group 09 Unit I (elements of statistics); background to all mensuration and inventory questions

Descriptive statistics, frequency distributions and diameter distributions
Probability and the binomial, Poisson and normal distributions
Sampling distributions, standard error and confidence intervals
Tests of significance: z, t, F and chi-square
Correlation and simple and multiple linear regression
Non-linear regression for tree allometry
Analysis of variance and basic experimental designs (CRD, RBD, Latin square)
Spreadsheets for field data
Introduction to R or Python for forest data
Data quality, field data recording and databases

Where the 60 questions fall

How our questions for ICAR AIEEA-PG spread across the units of Biometry, Statistics & Computing for Forestry. Difficulty: 21 easy, 39 medium, 0 hard.

Descriptive statistics, frequency distributions and diameter distributions	7
Probability and the binomial, Poisson and normal distributions	7
Tests of significance: z, t, F and chi-square	7
Analysis of variance and basic experimental designs (CRD, RBD, Latin square)	7
Spreadsheets for field data	7
Sampling distributions, standard error and confidence intervals	6
Correlation and simple and multiple linear regression	6
Introduction to R or Python for forest data	6
Data quality, field data recording and databases	6
Non-linear regression for tree allometry	1

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

1 · Descriptive statistics, frequency distributions and diameter distributions · easy

Plot volumes have a mean of 200 m³ ha⁻¹ and a standard deviation of 70 m³ ha⁻¹. What is the coefficient of variation?

2.9%
35%
70%
14%

Answer and working

B. 35%

CV = 70/200 × 100 = 35%. 2.9% inverts the ratio as a fraction of SD.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

2 · Probability and the binomial, Poisson and normal distributions · medium

Tree heights are normal with mean 20 m and SD 2 m. About what percentage of trees exceed 23 m?

15.9%
6.7%
2.3%
43.3%

Answer and working

B. 6.7%

z = (23 − 20)/2 = 1.5; upper-tail area 0.0668. 15.9% is for z = 1; 2.3% for z = 2; 43.3% is the area between 0 and 1.5.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

3 · Probability and the binomial, Poisson and normal distributions · easy

For a normal distribution, about what share of values lies within ±1.96 standard deviations of the mean?

95%
68%
99.7%
50%

Answer and working

A. 95%

68% within ±1σ, 95% within ±1.96σ, 99.7% within ±3σ.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

4 · Tests of significance: z, t, F and chi-square · medium

Of 100 seedlings, 70 are normal and 30 albino; a 3:1 ratio is expected. What is χ² and is the fit acceptable at 5% (critical value 3.84)?

1.33; the fit is rejected
1.33; fit acceptable
6.67; the fit is rejected
0.33; the fit is rejected

Answer and working

B. 1.33; fit acceptable

Expected 75 and 25: χ² = 25/75 + 25/25 = 1.33 < 3.84, so the 3:1 ratio is not rejected.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

5 · Correlation and simple and multiple linear regression · easy

The combined-variable volume equation is:

V = aD^bH^c
V = πD²/4
V = A(1 − e^(−kt))^c
V = b₀ + b₁D²H

Answer and working

D. V = b₀ + b₁D²H

It uses D²H as one predictor and is linear; aD^bH^c is Schumacher–Hall; the last is Chapman–Richards growth.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

6 · Non-linear regression for tree allometry · easy

An allometric equation y = aD^b becomes linear when:

Only y is squared
Both y and D are log-transformed
D is replaced by D²H
Both are divided by their means

Answer and working

B. Both y and D are log-transformed

ln y = ln a + b ln D is a straight line.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

7 · Spreadsheets for field data · easy

What is the per-hectare expansion factor for a 0.04 ha plot?

4
400
25
0.04

Answer and working

C. 25

10,000 m² / 400 m² = 25.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

8 · Spreadsheets for field data · medium

Which spreadsheet layout follows tidy-data principles for a tree inventory?

One row per plot with trees spread across columns
One row per tree per measurement, one column per variable
Merged cells grouping trees of the same species
Colour-coding damaged trees without a damage column

Answer and working

B. One row per tree per measurement, one column per variable

Each variable a column, each observation a row; colour and merged cells hide information.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

9 · Spreadsheets for field data · medium

What does a data validation rule on the diameter column (5–200 cm) achieve?

It converts diameters to basal area automatically
It computes the mean diameter of each plot
It corrects errors already in the data
It rejects implausible entries at the time of typing

Answer and working

D. It rejects implausible entries at the time of typing

Validation prevents entry errors; it does not fix earlier mistakes.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

10 · Introduction to R or Python for forest data · easy

Which R function fits an ordinary linear regression of height on diameter?

nls()
lm()
aov()
read.csv()

Answer and working

B. lm()

lm fits linear models; nls fits non-linear models; aov is ANOVA; read.csv reads data.

Further reading: See the manual sources: Freese 1967; Zar; Snedecor and Cochran; Gomez and Gomez; Husch et al.; Baskerville 1972

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