Question

1. you collect data on the number of eggs laid by a species of fly. most of the flies lay approximately 20-30 eggs, but a few lay no eggs and a few lay over 100. describe the shape of this distribution. which measure of spread would be best: standard deviation or iqr? why?

Explanation:

1. Shape of Distribution: Most flies lay 20 - 30 eggs (concentrated in the middle), with a few laying 0 (low outliers) and a few laying over 100 (high outliers). This creates a long tail on the right (and a small tail on the left), so the distribution is right - skewed (positively skewed).
2. Measure of Spread:

• Standard Deviation: Sensitive to outliers (since it uses the mean and squared deviations from the mean). Outliers (0 and >100 eggs) will inflate the standard deviation, making it an inaccurate measure of the "typical" spread of the main data cluster (20 - 30 eggs).
• IQR (Interquartile Range): Measures the spread of the middle 50% of data (between Q1 and Q3). It is resistant to outliers (does not depend on extreme values), so it better represents the spread of the majority of the data (the 20 - 30 egg cluster) without being affected by the few extreme values (0 or >100 eggs).

Answer:

• Shape of Distribution: The distribution is right - skewed (positively skewed). Most data is concentrated around 20 - 30 eggs, with a long tail to the right (from a few flies laying over 100 eggs) and a short tail to the left (from a few laying 0 eggs).
• Best Measure of Spread: The IQR is best. The distribution has outliers (flies laying 0 or over 100 eggs), and IQR is resistant to outliers (measures the spread of the middle 50% of data), while standard deviation is sensitive to outliers and would be distorted by the extreme values.