Questions and Answers
Using letter grades (A, B, C, D, and F) to classify student performance on an exam is an example of measurement on a(n) ______ scale of measurement.
ordinal
Determining a person's reaction time would involve measurement on a(n) ______ scale of measurement.
ratio
What additional info is obtained by measuring on an ordinal scale compared to a nominal scale?
the direction of the differences
Manipulating an independent variable involves:
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In a study where participants made fewer errors on a task when quiet background music was playing, the number of errors is the independent variable.
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A sample has a mean of M = 86. If one new person is added to the sample, what effect will it have on the sample mean?
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A sample of n = 6 scores has a mean of M = 5. One person with a score of X = 12 is added to the distribution. What is the mean for the new set of scores?
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A set of N = 10 scores has a mean of µ = 50. If 20 points are added to one of the scores, what is the new value for the population mean?
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Which of the following actions will always change the value of the mean?
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For a 100-point exam, a score of X = 65 is definitely above the median.
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If a sample has an odd number of scores, at least one individual will have a score exactly equal to the median.
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For a distribution with one or two extreme scores, the median is usually a more representative value than the mean.
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A sample has n = 5 scores: 2, 4, 5, 8, and 11. The median for the sample is 6.5.
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What is the purpose for obtaining a measure of central tendency?
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Explain why it is necessary to have more than one standard procedure for defining and measuring central tendency.
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What does σ (sigma) stand for?
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A sample of n = 25 scores has M = 20 and s² = 9. What is the sample standard deviation?
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The sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores. What is the variance for this sample?
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A population of scores has µ = 50 and σ = 5. If every score in the population is multiplied by 3, then what are the new values for the mean and standard deviation?
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For a particular sample, the largest distance (deviation) between a score and the mean is 11 points. The smallest distance between a score and the mean is 4 points. Therefore, the standard deviation _____.
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For a sample of n = 16 scores, how many scores are used to calculate the sample variance?
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What does s stand for?
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What does s² stand for?
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A set of 10 scores has SS = 90. If the scores are a sample, the sample variance is ____ and if the scores are a population, the population variance is ____.
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What does σ² stand for?
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The range and the standard deviation are both measures of distance.
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A positive deviation always indicates a score that is less than the mean.
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To calculate the variance for a sample, SS is divided by df = n - 1.
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In a population with a mean of μ = 40 and a standard deviation of σ = 8, a score of X = 46 would be an extreme value, far out in the tail of the distribution.
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After a researcher adds 5 points to every score in a sample, the standard deviation is found to be s = 10. The original sample had a standard deviation of s = 5.
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Study Notes
Measurement Scales
- Using letter grades for student performance exemplifies the ordinal scale of measurement.
- Measuring reaction time is conducted on a ratio scale.
Comparing Scales
- The ordinal scale provides direction of differences, which is not available in a nominal scale.
Independent Variables
- Manipulating an independent variable requires participants to be exposed to at least 2 levels of the variable.
Dependent and Independent Variables
- In a study on air-traffic control tasks, the number of errors is the dependent variable, not independent.
Effect on Sample Mean
- Adding a new individual to a sample with a mean of M = 86 will increase the sample mean.
- Adding a person with a score of X = 12 to a sample with a mean of M = 5 results in a new mean of M = 7.
- Increasing one score in a set of N = 10 scores from a mean of µ = 50 by 20 points results in a new population mean of 52.
Changing Mean Value
- Changing one score, adding, or removing scores will always change the mean value.
Median Facts
- A score of X = 65 is not necessarily above the median on a 100-point exam.
- In a sample with an odd number of scores, at least one score will equal the median.
- For distributions with extreme scores, the median is typically more representative than the mean.
Measures of Central Tendency
- The purpose of measuring central tendency is to determine an average or representative score for a group.
- Different standard procedures are necessary for defining central tendency due to skewed data.
Standard Deviation
- σ (sigma) denotes population standard deviation.
- For a sample with n = 25 scores, M = 20, and s² = 9, the sample standard deviation is 3.
- The sum of squared deviations, SS = 20, for a sample of n = 5 results in a variance of 5.
Population Changes
- If every score in a population with µ = 50 and σ = 5 is multiplied by 3, new mean and standard deviation become M = 150 and SD = 15.
Standard Deviation Range
- The standard deviation will be between 4 and 11 based on the largest and smallest distances from the mean.
Variance Calculation
- For a sample of n = 16 scores, all scores are used to calculate the sample variance.
- s stands for sample standard deviation, while s² stands for sample variance.
- For SS = 90 with a sample, the sample variance is 10; for a population, population variance is 9.
Measures of Distance
- Both the range and the standard deviation serve as measures of distance.
Deviation Insights
- A positive deviation indicates a score that is above the mean.
- Variance for a sample is calculated by dividing SS by n - 1.
Extreme Values and Constant Addition
- A score of X = 46 in a population of μ = 40 and σ = 8 is not an extreme value.
- Adding a constant value to every score does not affect the standard deviation.
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Description
Test your knowledge on different scales of measurement in statistics. This quiz covers topics such as ordinal, nominal, and ratio scales, helping you understand the distinctions and applications of each scale. Perfect for final exam review in statistics courses.
