#1
What is the formula for calculating the mean of a set of numbers?
Sum of numbers divided by the count of numbers
ExplanationAdd up all the numbers and divide by how many there are.
#2
In statistics, what does 'median' refer to?
The middle value when data is arranged in ascending order
ExplanationIt's the value at the center of a sorted list of numbers.
#3
What is the purpose of a histogram?
To display the distribution of continuous data
ExplanationIt shows the frequency distribution of continuous data.
#4
What is the formula for calculating the interquartile range (IQR)?
Third quartile minus first quartile
ExplanationIt measures the spread of middle 50% of the data.
#5
Which of the following is a measure of dispersion?
Standard deviation
ExplanationIt shows how spread out the numbers in a data set are.
#6
What is the formula for calculating standard deviation?
Square root of the variance
ExplanationIt's the square root of the average of the squared differences from the mean.
#7
What is the formula for calculating the variance of a data set?
Sum of squares of differences between each value and the mean, divided by the count of numbers
ExplanationIt's the average of the squared differences from the mean.
#8
In a normal distribution, what percentage of data falls within one standard deviation of the mean?
68%
ExplanationAbout two-thirds of the data falls within one standard deviation of the mean.
#9
What does 'correlation coefficient' measure?
Strength and direction of the linear relationship between two variables
ExplanationIt indicates how closely two variables are related.
#10
What is the difference between a parameter and a statistic?
Parameter refers to characteristics of a population, while statistic refers to characteristics of a sample
ExplanationParameters describe populations, while statistics describe samples.
#11
What is the formula for calculating the confidence interval for a population mean?
Sample mean plus or minus the product of the standard error and the critical value from the t-distribution
ExplanationIt gives a range of values that is likely to contain the population mean.
#12
What is a Type I error in hypothesis testing?
Incorrectly rejecting a true null hypothesis
ExplanationIt occurs when a true null hypothesis is rejected.
#13
What does 'outlier' mean in statistics?
A value that is much smaller or larger than the other values in a data set
ExplanationIt's a data point that differs significantly from other observations.
#14
What is the purpose of a scatter plot?
To display the relationship between two continuous variables
ExplanationIt helps visualize the relationship between two variables.
#15
What is the purpose of hypothesis testing?
To determine if there is enough evidence to reject or not reject a null hypothesis
ExplanationIt helps make decisions about populations based on sample data.
#16
What is a Type II error in hypothesis testing?
Incorrectly accepting a false null hypothesis
ExplanationIt occurs when a false null hypothesis is not rejected.
#17
Which statistical test is appropriate for comparing the means of two independent groups?
Independent samples t-test
ExplanationIt determines if there is a significant difference between the means of two groups.
#18
What does the 'P-value' represent in hypothesis testing?
Probability of observing a sample statistic as extreme as the one computed
ExplanationIt helps determine the strength of evidence against the null hypothesis.
#19
What is the formula for calculating covariance between two variables?
Product of differences between corresponding values and their means
ExplanationIt measures how two variables change together.
#20
Which of the following is a measure of skewness?
Coefficient of skewness
ExplanationIt quantifies the asymmetry of the distribution of a random variable.
#21
What is the formula for calculating the coefficient of variation?
Standard deviation divided by the mean, multiplied by 100
ExplanationIt standardizes the measure of dispersion by expressing it as a percentage.
#22
What is the central limit theorem?
States that the larger the sample size, the closer the sample mean approaches the population mean
ExplanationIt explains how the distribution of sample means approaches a normal distribution.
#23
What is the formula for calculating the coefficient of determination (R-squared)?
Correlation coefficient squared
ExplanationIt measures the proportion of variation in the dependent variable that is predictable from the independent variable.
#24
What is the formula for calculating the z-score of a data point?
(Data point - Mean) / Standard deviation
ExplanationIt measures how many standard deviations a data point is from the mean.
#25
What is the formula for calculating the sample size required for estimating a population mean with a specified margin of error and confidence level?
(Z-score * Standard deviation) / Margin of error
ExplanationIt helps determine the sample size needed to estimate a population mean.