Stats Topic 4

Question 1

Describing Distributions of Samples and Populations

Answer 1

• Distributions can be described using measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation, interquartile range).
• The shape of the distribution (e.g., normal, skewed) provides insight into the spread and symmetry of data.

Question 2

Central Tendency

Answer 2

• Mean: The arithmetic average of all values.
• Median: The middle value when data is arranged in order.
• Mode: The most frequently occurring value.

Question 3

Dispersion

Answer 3

• Range: Difference between maximum and minimum values.
• Variance: The average squared deviation from the mean.
• Standard Deviation: The square root of the variance; indicates average distance from the mean.
• Interquartile Range (IQR): Difference between upper and lower quartiles; useful for identifying spread without extreme values.

Question 4

Decision-making and Interpretation

Answer 4

• The mean is sensitive to extreme values, whereas the median is more robust in skewed distributions.
• Standard deviation is preferred when comparing variability across datasets.

Question 5

Standardized Scores (Z-Scores)

Answer 5

A Z-score represents how many standard deviations a value is from the mean.
Formula:

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Question 6

Interpretation of Z score

Answer 6

• A Z-score of 0 indicates a value is at the mean.
• Positive Z-scores indicate values above the mean, while negative Z-scores indicate values below the mean.
• Z-scores help in comparisons across different distributions.

Question 7

Likert scale

Answer 7

a rating scale used to measure survey participants’ opinions, attitudes, motivations, and more