Which average is computed without utilizing every value in the dataset?
Show answer Hide answer
Answer: E. Both C. and D.
Explanation
The median is determined by positional middle ranking, and the mode is determined by maximum frequency observation. Neither the median nor the mode requires calculating values using every single data point in the dataset. Consequently, both represent positional averages that remain unaffected by the exact magnitude of uncounted values. Positional averages are descriptive statistics whose values depend upon the relative position of items in sorted data. The arithmetic mean requires summing all individual data values, making it dependent on every single observation. Francis Galton and other statisticians analyzed the distinct properties of positional versus mathematical averages.
Option A is incorrect because the arithmetic mean explicitly requires utilizing every single value in the dataset. Option B is wrong because the geometric mean multiplies every individual data point together in its calculation. Option E correctly identifies that both median and mode share this property, making it superior to single choices.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Which case is true for hyper geometric distribution________________?
Show answer Hide answer
Answer: D. Both (b) & (c) but not (a)
Hypergeometric distributions model sampling without replacement from a finite population containing two groups. Removing items without replacement changes the population composition, causing success probabilities to chan...
Q2. Which of the measures listed rely on every single item in the series?
Show answer Hide answer
Answer: B. Standard Deviation
Standard deviation incorporates every single individual data point in its mathematical formula. Each observation contributes to calculating deviations from the arithmetic mean value. Omitting any single data value change...
Q3. Which value can never be assigned as a correlation coefficient_____________?
Show answer Hide answer
Answer: D. √3
Correlation coefficients are mathematically bound between negative one and positive one inclusive. The square root of three evaluates numerically to approximately 1.732 in decimal form. Because 1.732 exceeds the maximum...
Q4. Based on the heights of five classmates, you state the average for all university students is 67 inches. This is an example of ?
Show answer Hide answer
Answer: B. Inferential Statistics
Inferential statistics involves generalizing sample findings to a larger population. Using five classmates to estimate university-wide averages is an inference. This process uses probability theory to draw conclusions be...
Q5. Which of the following is not a property of the binomial distribution ?
Show answer Hide answer
Answer: D. Probability of success varies from trial to trial
A defining requirement of the binomial distribution is that the probability of success remains constant across trials. If the probability of success changes between trials, the experiment violates the core binomial model...
Q6. After asking five classmates about their height, you conclude the average height of all university students is 67 inches. This illustrates____________?
Show answer Hide answer
Answer: B. Inferential Statistics
Inferential statistics involves generalizing from a small sample to a larger population. Measuring five classmates constitutes a sample observation set used to estimate university norms. Drawing conclusions about all stu...