Math Problem Statement

You've been elected to the board, and to gather some information, you send out a survey to all residents about how often they think the board should meet each quarter. You get the following 60 responses: 3 2 1 2 3 2 3 2 4 1 1 3 4 3 4 3 3 2 1 1 4 3 4 4 1 4 4 4 2 3 2 3 3 3 3 3 4 4 1 3 1 1 3 1 3 1 1 3 1 2 2 1 1 1 2 2 2 2 3 4 Mean (¯¯¯X) = Round your answer to 2 decimal places as needed. Standard deviation (S) = Round your answer to 2 decimal places as needed. c) Determine the range of variation: (¯¯¯X−S,¯¯¯X+S) = Round your answers to 2 decimal places as needed. d) Calculate what percent of the data values are within one standard deviation of the mean. Hint: Create a histogram on paper and shade the included region(s) on your histogram to help visualize the shaded area and help with calculations. Total area of shaded region = Round your answer to 2 decimal places as needed. Percent of area within one standard deviation = Round your answer to 2 decimal places as needed.

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency
Standard Deviation
Range of Variation

Formulas

Mean (X̄) = Σx / n
Standard Deviation (S) = sqrt[Σ(x - X̄)^2 / (n-1)]
Range of Variation = (X̄ - S, X̄ + S)

Theorems

Empirical Rule (68-95-99.7 Rule)

Suitable Grade Level

Grades 9-12