C955 Applied Probability and Statistics - Set 1 - Part 1

Correct Answer: 6

The mean is the sum divided by the count. The values total 4 + 8 + 6 + 10 + 2 = 30, and 30 divided by 5 equals 6.

Correct Answer: 9

With five values already in order, the median is the middle value, which is the third one: 9.

Correct Answer: 5

With an even number of values, the median is the average of the two middle values: (4 + 6) divided by 2 equals 5.

Correct Answer: 5

The mode is the most frequently occurring value. The number 5 appears three times, more than any other value.

Correct Answer: Mean

The mean incorporates every value, so a single extreme observation pulls it substantially. The median depends only on position and resists outliers.

Correct Answer: Median

Income distributions are right-skewed with high outliers that inflate the mean. The median better represents the typical value in such distributions.

Correct Answer: 15

The range is the maximum minus the minimum: 20 minus 5 equals 15.

Correct Answer: The typical distance of values from the mean

Standard deviation quantifies spread by measuring how far observations typically fall from the mean. Larger values indicate greater dispersion.

Correct Answer: 0

With no variation, every value equals the mean, so all deviations are zero and the standard deviation is zero.

Correct Answer: Standard deviation is the square root of variance

Variance is the average squared deviation from the mean, and standard deviation is its square root, returning the measure to the original units.

Correct Answer: The mean is greater than the median

Right skew means a long tail of high values that pulls the mean upward, so the mean exceeds the median.

Correct Answer: They are approximately equal

In a perfectly symmetric unimodal distribution, the mean, median, and mode coincide at the center.

Correct Answer: The difference between the third and first quartiles

The IQR equals Q3 minus Q1 and describes the spread of the middle 50 percent of the data, making it resistant to outliers.

Correct Answer: The median

The line within the box marks the median. The box edges are the first and third quartiles.

Correct Answer: The entire group of interest about which conclusions are drawn

A population is the complete collection of all units of interest. A sample is a subset drawn from it to make inferences about the whole.

Correct Answer: A numerical characteristic of a population

A parameter describes a population, such as the population mean, while a statistic describes a sample and is used to estimate a parameter.

Correct Answer: A sample where every member of the population has an equal chance of selection

In simple random sampling every population member, and every possible sample of that size, is equally likely to be selected, supporting valid inference.

Correct Answer: Dividing the population into subgroups and sampling from each

Stratified sampling divides the population into homogeneous strata and samples within each, ensuring representation of all subgroups and often improving precision.

Correct Answer: It is likely to produce a biased, unrepresentative sample

Selecting readily available subjects systematically favors certain groups, so the sample may not represent the population and conclusions may be invalid.

Correct Answer: Systematic error from a sample that is not representative of the population

Selection bias occurs when the sampling process systematically over- or under-represents parts of the population, distorting results in a consistent direction.