#1
What is the median of the following set of numbers: 5, 8, 12, 16, 20, 22, 25?
20
ExplanationMiddle value of the sorted set.
#2
What is the mode of the following set of numbers: 4, 6, 8, 8, 10, 12, 12, 12, 14?
12
ExplanationMost frequently occurring value.
#3
What does 'standard deviation' measure in statistics?
The spread of data values
ExplanationDegree of dispersion.
#4
In a normal distribution, approximately what percentage of data falls within one standard deviation from the mean?
68%
ExplanationAbout two-thirds of the data.
#5
Which of the following is not a measure of central tendency?
Range
ExplanationMeasures the dispersion, not the centrality.
#6
In statistics, what does 'null hypothesis' refer to?
A hypothesis that states there is no significant difference or relationship between variables
ExplanationInitial assumption of no effect.
#7
What is the formula for calculating the z-score of a data point in a normal distribution?
(x - μ) / σ
ExplanationNumber of standard deviations from the mean.
#8
What is the formula to calculate the variance of a sample?
(Σ(x - μ)²) / (n - 1)
ExplanationAverage of the squared differences from the mean.
#9
What is the purpose of a p-value in hypothesis testing?
To determine the probability of obtaining the observed results if the null hypothesis is true
ExplanationAssessing the strength of evidence against the null hypothesis.
#10
What does the coefficient of determination (R-squared) represent in regression analysis?
The percentage of the total variation in the dependent variable explained by the independent variable(s)
ExplanationGoodness of fit of the regression line.
#11
What is the purpose of a confidence interval in statistics?
To estimate the range within which a population parameter is likely to lie
ExplanationIndicates the precision of an estimate.
#12
What is the formula for calculating the probability of an event A given event B, P(A|B), using the conditional probability formula?
P(A) / P(B)
ExplanationProbability of A given B occurred.