4. The forces that determine the size of groups (swarms) of social insects and the rates...

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4. The forces that determine the size of groups ("swarms") of social insects and the rates at which they grow are not well understood. Biologists have observed large variability in the size of swarms across species. In a study of the social wasp, Polybia occidentalis, investigators dismantled a nest of these insects and marked a few insects for future identification in new swarms. Twenty-five days after dismantling the original swarm they had located new swarms of wasps from the original colonies. The data below present the numbers of adults in the new swarms in two different years. "Drones" are fertile males that mate with the queen. Number of Drones. Swarm size in first year swarms 598 24 567 371 279 44 42 126 108 79 (a) (4 points) Calculate the values of these numerical summaries for the number of drones in the second year swarms: The mean: Swarm First Year Second Year Number of Drones Swarm size in second year swarms 355 691 278 719 (b) (5 points) Fill in the missing values of the table for the partial summary of data for the number of drones. First Year 152 156 Second Year The standard deviation: 100 Minimum Lower Quartile Median Upper Quartile Maximum 44 24 117 598 (c) (10 points) Construct comparative box plots of the numbers of drones in the swarms in the first and second years. 371 200 300 400 500 600 700 800 (d) (4 points) Using your box plots from part (c), compare the distributions of first and second year drones. Justify your comparisons by appealing to specific aspects of the box plots constructed. 4. The forces that determine the size of groups ("swarms") of social insects and the rates at which they grow are not well understood. Biologists have observed large variability in the size of swarms across species. In a study of the social wasp, Polybia occidentalis, investigators dismantled a nest of these insects and marked a few insects for future identification in new swarms. Twenty-five days after dismantling the original swarm they had located new swarms of wasps from the original colonies. The data below present the numbers of adults in the new swarms in two different years. "Drones" are fertile males that mate with the queen. Number of Drones. Swarm size in first year swarms 598 24 567 371 279 44 42 126 108 79 (a) (4 points) Calculate the values of these numerical summaries for the number of drones in the second year swarms: The mean: Swarm First Year Second Year Number of Drones Swarm size in second year swarms 355 691 278 719 (b) (5 points) Fill in the missing values of the table for the partial summary of data for the number of drones. First Year 152 156 Second Year The standard deviation: 100 Minimum Lower Quartile Median Upper Quartile Maximum 44 24 117 598 (c) (10 points) Construct comparative box plots of the numbers of drones in the swarms in the first and second years. 371 200 300 400 500 600 700 800 (d) (4 points) Using your box plots from part (c), compare the distributions of first and second year drones. Justify your comparisons by appealing to specific aspects of the box plots constructed.

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a Me an 22 67 Standard Dev iation 6 00 b 24 90 c d The box plots for first and secondyear dro... View the full answer