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Questions and Answers
A researcher is studying the effect of different teaching methods on student test scores. They calculate descriptive statistics for each group. What is the primary purpose of using descriptive statistics in this context?
A researcher is studying the effect of different teaching methods on student test scores. They calculate descriptive statistics for each group. What is the primary purpose of using descriptive statistics in this context?
- To determine if the different teaching methods have a statistically significant effect on test scores.
- To generalize the findings to a larger population of students.
- To predict future test scores based on the teaching methods used.
- To summarize and describe the test score data for each teaching method group. (correct)
In a dataset of student ages, which measure of central tendency would be most affected by the presence of a few extremely old students (outliers)?
In a dataset of student ages, which measure of central tendency would be most affected by the presence of a few extremely old students (outliers)?
- Mean (correct)
- Mode
- Interquartile Range
- Median
A data set includes the following values: 2, 3, 3, 4, 5, 6, 7, 8, 9. What is the median of this data set?
A data set includes the following values: 2, 3, 3, 4, 5, 6, 7, 8, 9. What is the median of this data set?
- 3
- 5.44
- 5 (correct)
- 6
For a symmetrical distribution, which of the following statements is true regarding the relationship between the mean, median, and mode?
For a symmetrical distribution, which of the following statements is true regarding the relationship between the mean, median, and mode?
A researcher wants to quickly determine the spread of scores in a dataset. Which measure of dispersion is simplest to calculate?
A researcher wants to quickly determine the spread of scores in a dataset. Which measure of dispersion is simplest to calculate?
A dataset of test scores has a mean of 75 and a standard deviation of 5. Approximately what percentage of scores fall between 65 and 85, assuming a normal distribution?
A dataset of test scores has a mean of 75 and a standard deviation of 5. Approximately what percentage of scores fall between 65 and 85, assuming a normal distribution?
Which of the following is LEAST likely to be influenced by outliers in a data set?
Which of the following is LEAST likely to be influenced by outliers in a data set?
A researcher measures the happiness level of individuals on a scale of 1 to 10. What type of variable is 'happiness level' in this scenario?
A researcher measures the happiness level of individuals on a scale of 1 to 10. What type of variable is 'happiness level' in this scenario?
What does a large standard deviation indicate about a dataset?
What does a large standard deviation indicate about a dataset?
A researcher is analyzing the distribution of income in a city. The distribution has a long tail extending towards the higher income values. What type of skew does this distribution exhibit?
A researcher is analyzing the distribution of income in a city. The distribution has a long tail extending towards the higher income values. What type of skew does this distribution exhibit?
The interquartile range (IQR) is a measure of:
The interquartile range (IQR) is a measure of:
For a normally distributed dataset, approximately what percentage of data points fall within one standard deviation of the mean?
For a normally distributed dataset, approximately what percentage of data points fall within one standard deviation of the mean?
A set of test scores is as follows: 60, 70, 70, 80, 90. What is the mode of this set of scores?
A set of test scores is as follows: 60, 70, 70, 80, 90. What is the mode of this set of scores?
Which of the following is a measure of dispersion?
Which of the following is a measure of dispersion?
If a distribution has a kurtosis value greater than zero, it is called:
If a distribution has a kurtosis value greater than zero, it is called:
A student scores 80 on a test. The mean score is 70, and the standard deviation is 5. What is the student's z-score?
A student scores 80 on a test. The mean score is 70, and the standard deviation is 5. What is the student's z-score?
What type of statistics would be used to analyze the relationship between the type of note-taking method (longhand vs. laptop) and exam performance?
What type of statistics would be used to analyze the relationship between the type of note-taking method (longhand vs. laptop) and exam performance?
Which type of variable is 'eye color' (e.g., blue, brown, green)?
Which type of variable is 'eye color' (e.g., blue, brown, green)?
If a distribution is negatively skewed, which of the following relationships between the mean, median, and mode is most likely?
If a distribution is negatively skewed, which of the following relationships between the mean, median, and mode is most likely?
A researcher wants to compare the variability in exam scores between two different classes. Which statistic would be most appropriate for this purpose?
A researcher wants to compare the variability in exam scores between two different classes. Which statistic would be most appropriate for this purpose?
Flashcards
Descriptive statistic
Descriptive statistic
A type of statistic that describes data through central tendency, dispersion, skew, and kurtosis.
Central tendency
Central tendency
A measure of the 'average' value in a dataset.
Dispersion Statistic
Dispersion Statistic
A measure of how spread out the values are in a dataset.
Mean
Mean
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Median
Median
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Mode
Mode
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Range
Range
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Interquartile range (IQR)
Interquartile range (IQR)
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Variance
Variance
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Standard Deviation
Standard Deviation
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Nominal variables
Nominal variables
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Skew
Skew
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Kurtosis
Kurtosis
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Standard score (z score)
Standard score (z score)
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Study Notes
- Descriptive statistics are being examined
- Central tendency, dispersion, and distributions are covered
- JASP is used for descriptive statistics
Research Study
- Note-taking format affects lecture content recall
- Note-taking format impacts memory of exam material
Types of Statistics
- Descriptive statistics involve central tendency
- Inferential statistics exist
Central Tendency
- Central tendency is the measure of the typical value for a probability distribution
Mean
- The mean is the the average of a set of values
- The mean is calculated by summing all values and dividing by the number of values
- Formula: 𝑋 = (Σ X_i) / N
Median
- The median is the middle value of an ordered data set
- For N=15 observations, the median is the 8th value
- For N=14 observations, the median is the average of the 7th and 8th values
Median vs. Mean
- The median of a data set with an outlier of 500 is 40
- This is the same as a data set without the outlier
Mode
- The mode is the most frequently occurring value in a data set
Nominal Variables
- Nominal variables can also be called categorical variables
- Counts or frequencies can describe categorical variables
- An example of a categorical variable includes degree choice (Psychology, Engineering, Business, Arts, Other)
- Unit of measure is student
- Mode is a type of nominal variable
Dispersion
- Dispersion is the extent to which a distribution is stretched or squeezed
Range
- The range is the difference between the largest and smallest values in a data set
- The range is calculated as: Xmax - Xmin
Interquartile Range
- The interquartile range (IQR) is the difference between the 25th and 75th percentiles
- The median is the 50th percentile
- 25% of the data lies below the 25th percentile and one quarter of the data is above the 75th percentile
- The IQR represents the range spanned by the middle half of the data
Variance
- Variance is the mean squared deviation
- Var(𝑋) = Σ(X_i − 𝑋)^2 / N, where N is the number of observations
Standard Deviation
- Standard deviation is the root mean square deviation
- s = √[Σ(X_i − 𝑋)^2 / N]
- 68% of the data falls within 1 standard deviation of the mean
- 95% of the data falls within 2 standard deviations of the mean
- 99.7% of the data falls within 3 standard deviations of the mean
Distributions
- Distributions include skew and kurtosis
Skewness
- No skew (normal distribution): mean = median = mode
- Negative skew (left skew): tail is on the left; Mean < Median < Mode
- Positive skew (right skew): tail is on the right; Mode < Median < Mean
Kurtosis
- Platykurtic ('too flat'): Kurtosis < 0
- Mesokurtic: Kurtosis ≈ 0
- Leptokurtic ('too pointy'): Kurtosis > 0
Standard (z) Score
- Standard score indicates how many standard deviations an element is from the mean
- z_i = (X_i - X) / s
- Example: a score of 55, when the mean is 40.1 and standard deviation is 6.6, has a 𝑍 score of 2.26, and lies 2.26 Standard Deviations above the mean
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