Math Problem Statement

The data to the right contain the​ per-capita energy​ consumption, in​ kilowatt-hours, for each of the 20 provinces of a nation. Complete parts​ (a) through​ (c) below. 23 comma 460 21 comma 394 20 comma 699 19 comma 648 18 comma 218

18 comma 108 18 comma 098 18 comma 035 17 comma 927 17 comma 688 15 comma 058 14 comma 604 13 comma 818 13 comma 536 12 comma 890 12 comma 481 11 comma 841 9 comma 784 6 comma 528 6 comma 185 Question content area bottom Part 1 a. Compute the​ mean, variance, and standard deviation for the population. The population mean is muequals    simplify the answer

Solution

The population mean is 15,50015,500 kilowatt-hours.

  • The population variance is approximately 20,865,851.920,865,851.9 kilowatt-hours squared.
  • The population standard deviation is approximately 4,567.924,567.92 kilowatt-hours.

Would you like to go over the detailed steps for these calculations or have any questions?

Here are 5 related questions to expand on this:

  1. How would the mean change if the highest value were removed from the data set?
  2. What is the difference between population and sample variance?
  3. How do you interpret standard deviation in the context of energy consumption?
  4. Can you calculate the coefficient of variation using the data provided?
  5. How would you calculate the z-score for a particular province's energy consumption?

Tip: Always use the population variance formula when working with the full data set rather than a sample.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Measures of Central Tendency
Measures of Dispersion

Formulas

Mean formula: μ = Σx / N
Variance formula: σ² = Σ(x - μ)² / N
Standard deviation formula: σ = √σ²

Theorems

Basic Properties of Variance and Standard Deviation

Suitable Grade Level

Grades 10-12

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