Variation.12Aug2025.Lecture8
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Biology
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Professional Development
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J Arro
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4 Slides • 18 Questions
1
12Aug2025.Lecture8
Measures of Variation
By J Arro
2
Multiple Choice
Two lakes both have fish averaging 10 cm in length. In Lake A, all fish are exactly 10 cm. In Lake B, fish range from 6 to 14 cm. Which lake is likely to have a more complex food web?
Lake A
Lake B
Both equally complex
Cannot tell without knowing the mean
3
Multiple Choice
What is the range of fish lengths in Lake B (6, 8, 10, 12, 14 cm)?
4
6
8
10
4
Multiple Choice
IQR is the spread of the middle 50% of the data.
For the same fish lengths (6, 8, 10, 12, 14 cm), what is the Interquartile Range (IQR)?
4 cm
6 cm
8 cm
2 cm
5
Multiple Choice
In a boxplot comparing Lake A and Lake B, which lake’s plot would have a wider box and whiskers?
Lake A
Lake B
Both the same
Cannot determine
6
Multiple Choice
Which statement about Standard Deviation (SD) is true?
High SD means values are closer to the mean.
Low SD means data is more spread out.
High SD means values are more spread out
SD is unaffected by extreme values.
7
Multiple Choice
Why might a plant species with high variation in chemical defenses be more resilient?
All plants taste the same to herbivores.
Some plants deter herbivores while others don’t, supporting varied interactions
Herbivores can eat everything equally.
Variation confuses predators but harms the plants.
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Multiple Choice
Which statistical fact explains why two datasets can have the same mean but different ecological outcomes?
The datasets have different variances.
The datasets have different medians.
The datasets have different sums.
The datasets have different modes.
9
Multiple Choice
A histogram with a long tail to the right is described as:
Left-skewed
Right-skewed
Symmetrical
Normal
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Multiple Choice
In a fish population, most individuals are small but a few grow very large. This size distribution is:
Symmetrical
Right-skewed
Left-skewed
Bell-shaped
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Multiple Choice
Why might fisheries management that uses only the average size be risky?
It ignores variation that affects breeding capacity.
It overestimates the number of large fish.
It underestimates the smallest fish.
It has no effect if the mean is correct.
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Multiple Choice
Which best describes the role of variation in data analysis?
Variation is unwanted noise.
Variation contains important information.
Variation should always be minimized.
Variation means the data is invalid.
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Word Cloud
In one word, why does variation matter?
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Word Cloud
In one word, what is a mean?
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Word Cloud
In one word, what is a standard deviation?
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VARIATION part II
14Aug2025
17
Multiple Choice
Bridge idea: Which pairing best builds intuition for the bell curve?
Pie chart + scatter plot
Histogram (raw) + density line (smooth) when there is variation
Boxplot alone
Bar plot of categories
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Feature | Bar plot | Histogram |
|---|
Data type (x-axis) | Categorical (factor/character) or precomputed summaries | Numeric (continuous) values |
What height means | Count per category (geom_bar), or a supplied value/mean (geom_col) | Count or density in each bin (range) |
Bar spacing | Gaps between categories | Touching bars (adjacent bins) |
Area interpretation | Not meaningful (nominal scale) | Area ≈ proportion; density integrates to 1 |
Typical ggplot layer | geom_bar() (counts) or geom_col() (precomputed) | geom_histogram() (optionally aes(y = after_stat(density))) |
Good add-on | Labels, reorder, percentages | Density curve (geom_density) for smoothing |
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==== Data Visualization: Histograms and Bar Plots ====
20
Multiple Choice
When all observed values are the same (e.g., all 155 cm), the sample SD is…
Negative
0
Undefined
Always 1
21
Multiple Choice
The sample variance (s²) is best described as:
The average of raw deviations from the mean
The average of squared deviations from the mean (with a small-sample correction)
The square of the mean
The average absolute deviation
22
Multiple Choice
Which statement is true about variance and standard deviation?
Both have the same units as the data
Variance has squared units; SD is the square root of variance and has the original units
Both are unitless
SD has squared units; variance has the original units
12Aug2025.Lecture8
Measures of Variation
By J Arro
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