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Worksheets3 Stats - Variance
Total questions: 29
Worksheet time: 15mins
Why is the average only "half the story" in data analysis?
Because it excludes information about central tendency.
Because it considers only a single value in the dataset.
Because it does not include information about variability.
Because it includes outliers as part of its calculation.
What are the two common measures of variability?
Mean and standard deviation.
Range and variance.
Range and standard deviation.
Interquartile range and variance.
How is the range calculated?
By subtracting the mean from the highest score in the dataset.
By adding the lowest and highest scores together.
By subtracting the lowest score from the highest score in the dataset.
By dividing the sum of scores by the number of observations.
What are the limitations of the range?
It accounts for all scores but ignores outliers.
It considers only the lowest and highest scores, is vulnerable to outliers, and can vary with sample size.
It fails to capture the distribution curve.
It underestimates the standard deviation.
What is the interquartile range?
The difference between the mean and the median.
The range of all scores after removing outliers.
The range of the middle 50% of scores after excluding the lowest and highest quartiles.
The range of values that appear most frequently.
How is the interquartile range calculated?
Rank scores, exclude the highest and lowest scores, and subtract the smallest from the largest.
Rank scores, exclude the lowest 25% and highest 25%, then subtract the lowest from the highest of the remaining scores.
Divide the total range into four equal parts and calculate the mean of each.
Subtract the mean from the median.
What does variance measure?
The range of scores in a dataset.
How spread out data are around the mean.
The median distance of scores from the mean.
The steepness of the data distribution.
Why are deviations squared in variance calculations?
To highlight the outliers.
To make the calculations more complex.
To avoid negative values canceling out positive values.
To ensure the variance is higher than the range.
How is variance calculated?
Square each score’s deviation from the mean, sum them, and divide by the total number of scores.
Subtract the smallest score from the largest and square the result.
Find the average deviation of scores from the median.
Take the standard deviation and multiply by itself.
What is the standard deviation (SD)?
A measure of the steepness of the data distribution.
The square root of variance, representing the average amount by which scores deviate from the mean.
The range of the middle 50% of the dataset.
The median distance of scores from the mean.
What does a small SD indicate?
That scores are widely spread from the mean.
That most scores cluster closely around the mean.
That the dataset has outliers.
That the range is larger than expected.
What does a large SD indicate?
That most scores cluster closely around the mean.
That the dataset has a leptokurtic distribution.
That scores are widely spread from the mean.
That the mean and median are equal.
In a normal distribution, what proportion of scores falls within one SD of the mean?
99.74%.
95.44%.
68.26%.
34.13%.
In a normal distribution, what proportion of scores falls within two SDs of the mean?
95.44%.
68.26%.
99.74%.
34.13%.
What does a skewed distribution indicate?
That the data has no variability.
That the data is not symmetrical and is lopsided to the left (negative skew) or right (positive skew).
That the dataset has a leptokurtic distribution.
That the mean and median are equal.
What happens to the mean and median in a negatively skewed distribution?
The mean and median are equal to the mode.
The mean and median are larger than the mode.
The mean and median are smaller than the mode.
The mean and median are unaffected.
What happens to the mean and median in a positively skewed distribution?
The mean and median are smaller than the mode.
The mean and median are unaffected.
The mean and median are equal to the mode.
The mean and median are larger than the mode.
What does kurtosis measure?
The steepness or flatness of a data distribution.
The variability in a dataset.
The central tendency of scores.
The range of the middle 50% of scores.
What is a mesokurtic distribution?
A normal, bell-shaped curve.
A steep curve with heavy tails.
A flat curve with light tails.
A positively skewed distribution.
What is a leptokurtic distribution?
A flat curve with light tails.
A steep curve with heavy tails.
A normal, bell-shaped curve.
A negatively skewed distribution.
What is a platykurtic distribution?
A steep curve with heavy tails.
A normal, bell-shaped curve.
A flat curve with light tails.
A dataset with no variability.
How can you determine if a dataset is normally distributed?
By inspecting the median and mode, checking standard deviation, and examining outliers.
By inspecting the mean, median, and mode, examining histograms, checking skewness and kurtosis, or performing statistical tests.
By calculating variance and interquartile range.
By performing a t-test for variability and comparing kurtosis to skewness.
What is considered an acceptable range for skewness and kurtosis values?
Between -3 and +3.
Between -2 and +2.
Between 0 and +1.
Between -1 and +1.
What are the two tests of normality available in SPSS?
Kolmogorov-Smirnov test and Levene's test.
Shapiro-Wilk test and Bartlett's test.
Kolmogorov-Smirnov test and Shapiro-Wilk test.
Kruskal-Wallis test and Mann-Whitney test.
Which test of normality should be used for a sample size smaller than 40?
Kolmogorov-Smirnov test.
Bartlett's test.
Shapiro-Wilk test.
Levene's test.
Which test of normality should be used for a sample size larger than 40?
Shapiro-Wilk test.
Kolmogorov-Smirnov test.
Kruskal-Wallis test.
Mann-Whitney test.
What does a non-significant result in a normality test indicate?
That there is no statistically significant difference between the dataset and a perfect normal distribution.
That the dataset is highly variable.
That the dataset has a leptokurtic distribution.
That the mean and median are not equal.
What is a potential issue with normality tests in small samples?
They may lack power and fail to detect non-normality.
They may overestimate variability in the dataset.
They may fail to measure kurtosis accurately.
They cannot detect positive skewness.
What is a potential issue with normality tests in large samples?
They may fail to detect deviations from normality.
They may detect even minor deviations from normality as statistically significant.
They may misclassify kurtosis as skewness.
They cannot differentiate between positive and negative skewness.
