Skip to main content
Sign in Register
Sarkari MCQs Government Exam Question Bank
Question no. 93304

For x = 4 within the distribution 2, 3, 4, 5, 6, the sum of squared deviations from x will be______________?

Select your answer for: For x = 4 within the distribution 2, 3, 4, 5, 6, the sum of squared deviations from x will be______________?
Show answer

Answer: B. 10

Explanation

The arithmetic mean of the given numbers 2, 3, 4, 5, and 6 is exactly 4. Calculating squared deviations gives values of 4, 1, 0, 1, and 4 relative to the mean. Summing these individual squared differences together results in a total value equal to exactly 10. Squared deviations measure the dispersion of data points around a chosen central benchmark value. The formula for squared deviations involves subtracting the mean and squaring each resulting difference. This calculation forms the foundational mathematical basis for computing variance and standard deviation.

Data analysts compute squared deviations to understand how tightly clustered observations are around their average. Minimizing the sum of squared deviations is a core principle behind ordinary least squares regression. Quality control engineers use spread measures to detect abnormal variations in manufacturing output processes. Option A is incorrect because basic arithmetic mistakes lead to an inaccurate sum of squares. Option C underestimates the total dispersion by omitting several squared distance calculations entirely. Option D overestimates the dispersion due to incorrect arithmetic during the individual squaring steps.

Subject
Mathematics
Category
Statistics
Topic
—
Difficulty
medium

Related questions

Mathematics Statistics
medium

Q1. Variance is minimized when deviations are measured relative to______________?

Select your answer for: Variance is minimized when deviations are measured relative to______________?
Save
Show answer

Answer: B. Mean

The sum of squared differences between data points and a constant is minimized at the mean. Calculus shows that taking the derivative of squared error with respect to the constant yields the mean. No other central locati...

Mathematics Statistics
medium

Q2. If P(A/B)=1/4 alongside P(A∩B) =1/5, what is P(B) ________________?

Select your answer for: If P(A/B)=1/4 alongside P(A∩B) =1/5, what is P(B) ________________?
Save
Show answer

Answer: A. 4/5

Conditional probability equals the intersection probability divided by the marginal probability of the conditioning event. Rearranging the conditional probability formula shows that the probability of B equals intersecti...

Mathematics Statistics
medium

Q3. When variables x and y remain mutually independent, their correlation coefficient equals _____________?

Select your answer for: When variables x and y remain mutually independent, their correlation coefficient equals _____________?
Save
Show answer

Answer: D. 0

Independent variables show no linear relationship and yield a correlation coefficient of zero. Zero correlation means knowing the value of one variable provides no predictive power. The mathematical formulation of covari...

Mathematics Statistics
medium

Q4. A distribution whose right tail extends further than its left tail is termed _________________?

Select your answer for: A distribution whose right tail extends further than its left tail is termed _________________?
Save
Show answer

Answer: B. Positively Skewed

Skewness direction is determined by the longer trailing tail of a frequency distribution. A right side extension indicates a long tail stretching toward higher numerical values. Statisticians formally designate this dist...

Mathematics Statistics
medium

Q5. Under what condition does Var(T2)_______________?

Select your answer for: Under what condition does Var(T2)_______________?
Save
Show answer

Answer: A. Efficient

Efficiency in statistical inference refers strictly to having the smallest possible variance among estimators. An estimator is deemed efficient if no other unbiased estimator achieves a lower sampling variance. The Cramé...