#1
What is the median of the following set of numbers: 3, 6, 9, 12, 15?
10.5
ExplanationMiddle value; average of 10 and 11.
#2
Which measure of central tendency is most affected by outliers?
Mean
ExplanationSensitive to extreme values; affected by outliers.
#3
What is the probability of rolling a prime number on a fair six-sided die?
1/6
ExplanationOne prime number (2, 3, 5) out of six possible outcomes.
#4
Which of the following is NOT a measure of dispersion?
Median
ExplanationMeasure of central tendency; not a measure of spread.
#5
In a statistical experiment, what does 'random sampling' refer to?
Ensuring every individual in the population has an equal chance of being selected for the sample
ExplanationSelection process without bias; every individual has an equal chance.
#6
What is the formula for calculating standard deviation?
√(Σ(xi - x̄)² / N)
ExplanationSquare root of the average squared deviation from the mean.
#7
In a normal distribution, what percentage of data falls within one standard deviation from the mean?
68%
ExplanationApproximately two-thirds of data within one standard deviation.
#8
What is the formula for calculating the z-score of a data point?
(x - μ) / σ
ExplanationStandardized measure indicating the number of standard deviations from the mean.
#9
What does the p-value represent in hypothesis testing?
The probability of obtaining the observed results, or more extreme, assuming the null hypothesis is true
ExplanationProbability of observed results under the assumption that the null hypothesis is true.
#10
What is the formula for calculating the coefficient of determination (R-squared) in linear regression?
1 - (Σ(yi - ŷi)² / Σ(yi - ȳ)²)
ExplanationProportion of variance explained by the regression model.
#11
What is the formula for calculating the coefficient of variation?
(Standard Deviation / Mean) * 100
ExplanationRelative measure of dispersion; expressed as a percentage.
#12
What is the formula for calculating the covariance between two variables X and Y?
Σ(xi * yi) / N
ExplanationMeasure of joint variability; sum of product divided by sample size.
#13
What is the formula for the probability density function (PDF) of a normal distribution?
(1 / (σ * √(2π))) * e^(-((x - μ)² / (2σ²)))
ExplanationBell-shaped curve; likelihood of observing a specific value.
#14
What is the formula for the confidence interval of the population mean with a known population standard deviation?
(x̄ ± (z * (σ / √n)))
ExplanationRange within which the true population mean is likely to fall.
#15
What is the formula for calculating the harmonic mean?
N / Σ(1 / xi)
ExplanationReciprocal of the arithmetic mean of reciprocals.