Math Problem Statement
A small animal veterinarian reviews her records for the day and notes that she has seen eight dogs and eight cats with the following weights (in pounds).
Dogs: 12, 21, 39, 44, 52, 61, 74, 102
Cats: 4, 5, 8, 12, 15, 19, 23, 23
a. Before analyzing these data sets, make a conjecture about which set has the larger mean, median, and standard deviation. Explain your reasoning.
b. Compute the mean and standard deviation of each set.
Question content area bottom
Part 1
a. Make correct conjectures below about which set has the larger mean, median, and standard deviation. Choose the correct answer below.
A.
The mean, median, and standard deviation are all higher for cats because there is less variation in the weights, so the average value, middle value, and spread must be larger.
B.
The mean and median are higher for cats because there is less variation in the weights. The standard deviation is higher for dogs because there is more variation in the weights.
C.
The mean, median, and standard deviation are all higher for dogs because most of the weights are larger, so the average value, middle value, and spread must be larger.
D.
The mean and median are higher for dogs because most of the weights are larger, so the average value and middle value must be larger. The standard deviation is higher for cats because there is more variation in the weights.
Solution
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Measures of Central Tendency
Standard Deviation
Formulas
Mean: (Sum of all values) / (Number of values)
Sample Standard Deviation: sqrt( (1 / (n - 1)) * sum((x_i - mean)^2) )
Theorems
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Suitable Grade Level
Grades 10-12
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