Engineering Data Analysis

Question 1

1. The mean of a sample data set is 40 and the standard deviation is 6. Find the coefficient of variation (CV).
   A. 10% B. 12% C. 15% D. 20%

Answer 1

✅ Answer: C – 15%
Justification: CV = (6 / 40) × 100 = 15%; measures relative dispersion of data.

Question 2

2. If the sum of deviations from mean is always ___.
   A. Zero B. One C. Negative D. Varies

Answer 2

✅ Answer: A – Zero
Justification: Σ(x − x̄) = 0 for any set — a property of the arithmetic mean.

Question 3

3. Which measure of central tendency is least affected by extreme values?
   A. Mean B. Median C. Mode D. Range

Answer 3

✅ Answer: B – Median
Justification: Median depends only on middle position, not on magnitude of extreme values.

Question 4

4. In a normal distribution, mean = median = mode. What is the skewness?
   A. Zero B. Positive C. Negative D. Undefined

Answer 4

✅ Answer: A – Zero
Justification: Perfect symmetry → no skewness.

Question 5

5. For a normal curve, approximately what percent of data lies within ± 1 σ?
   A. 50% B. 68% C. 95% D. 99.7%

Answer 5

✅ Answer: B – 68%
Justification: Empirical Rule: ±1σ = 68%, ±2σ = 95%, ±3σ = 99.7%.

Question 6

6. The square of standard deviation is ___.
   A. Mean B. Variance C. Range D. Coefficient of Variation

Answer 6

✅ Answer: B – Variance
Justification: σ² = variance, basic formula of dispersion.

Question 7

7. A survey shows mean = 70, σ = 10. Find z if x = 85.
   A. 1.0 B. 1.2 C. 1.5 D. 1.7

Answer 7

✅ Answer: C – 1.5
Justification: z = (x − μ)/σ = (85 − 70)/10 = 1.5.

Question 8

8. If two variables increase together, the correlation coefficient is ___.
   A. Negative B. Zero C. Positive D. Undefined

Answer 8

✅ Answer: C – Positive
Justification: Direct relationship → r > 0.

Question 9

9. Correlation coefficient (r) always lies between ___.
   A. −1 to 0 B. −1 to +1 C. 0 to 1 D. 0 to ∞

Answer 9

✅ Answer: B – −1 to +1
Justification: r measures strength and direction of linear relation.

Question 10

10. A data set has values 3, 5, 7, 7, 8. Find the mode.
    A. 3 B. 5 C. 7 D. 8

Answer 10

✅ Answer: C – 7
Justification: Most frequent value is 7.

Question 11

11. A histogram is used to represent what type of data?
    A. Nominal B. Ordinal C. Discrete/Continuous D. Qualitative

Answer 11

✅ Answer: C – Discrete/Continuous
Justification: Histogram visualizes frequency distribution of numerical data.

Question 12

12. Which measure represents the “middle 50%” of data?
    A. Standard Deviation B. Range C. Quartile Deviation D. Mean Deviation

Answer 12

✅ Answer: C – Quartile Deviation
Justification: (Q3 − Q1)/2 covers central 50% spread.

Question 13

13. If mean = 30, mode = 25, find median using Empirical Relation.
    A. 27 B. 28 C. 29 D. 30

Answer 13

✅ Answer: B – 28
Justification: Mode ≈ 3Median − 2Mean → 25 = 3M − 60 → M = 28.33.

Question 14

14. Find the probability of getting a head in one coin toss.
    A. 0.25 B. 0.5 C. 0.75 D. 1

Answer 14

✅ Answer: B – 0.5
Justification: One favorable event out of two possible.

Question 15

15. If r = 0, then the two variables are ___.
    A. Perfectly related B. Independent C. Negatively related D. Non-linear

Answer 15

✅ Answer: B – Independent
Justification: No linear relationship exists (uncorrelated).

Question 16

16. A bell-shaped curve indicates a ___ distribution.
    A. Skewed B. Uniform C. Normal D. Exponential

Answer 16

✅ Answer: C – Normal
Justification: Symmetrical bell curve = normal distribution.

Question 17

17. If the probability of failure is 0.3, what is the probability of success?
    A. 0.5 B. 0.6 C. 0.7 D. 0.8

Answer 17

✅ Answer: C – 0.7
Justification: P(success) = 1 − P(failure) = 0.7.

Question 18

18. A data has values 2, 4, 6, 8, 10. Find the mean.
    A. 5 B. 6 C. 7 D. 8

Answer 18

✅ Answer: B – 6
Justification: Σx/n = 30/5 = 6.

Question 19

19. Which graph is best for showing cumulative frequency?
    A. Histogram B. Ogive C. Bar Chart D. Pie Chart

Answer 19

✅ Answer: B – Ogive
Justification: Ogive plots cumulative frequencies vs. class boundaries.

Question 20

20. If five numbers have a mean of 8, their sum is ___.
    A. 8 B. 16 C. 24 D. 40

Answer 20

✅ Answer: D – 40
Justification: Σx = n × mean = 5 × 8 = 40.

Question 21

21. The best fit line in regression minimizes ___.
    A. Errors B. Sum of Squares of Errors C. Variance D. Residual Mean

Answer 21

✅ Answer: B – Sum of Squares of Errors
Justification: Least Squares Method criterion.

Question 22

22. For a normal distribution, the area under the curve equals ___.
    A. 0.5 B. 1 C. 100 D. Undefined

Answer 22

✅ Answer: B – 1
Justification: Total probability = 1.

Question 23

23. A statistic computed from sample data used to estimate population parameter is called ___.
    A. Estimator B. Variable C. Population Mean D. Statistic Mean

Answer 23

✅ Answer: A – Estimator
Justification: It estimates unknown population parameter.

Question 24

24. What happens to standard deviation if all data values increase by a constant k?
    A. Increases B. Decreases C. Unchanged D. Doubles

Answer 24

✅ Answer: C – Unchanged
Justification: Shift affects mean but not spread.

Question 25

25. In a normally distributed data, approximately 95% of values lie within ___. A. ±1σ B. ±2σ C. ±3σ D. ±4σ

Answer 25

✅ Answer: B – ±2σ Justification: Empirical Rule → 95% within two standard deviations.