{
  "problem": "You have found the following ages (in years) of 4 meerkats. The meerkats are randomly selected from the 39 meerkats at your local zoo: $ 1,\\enspace 9,\\enspace 13,\\enspace 2$ Based on your sample, what is the average age of the meerkats? What is the variance? You may round your answers to the nearest tenth.",
  "hints": [
    "Because we only have data for a small sample of the 39 meerkats, we are only able to estimate the population mean and variance by finding the",
    "sample mean",
    "$({\\overline{x}})$",
    "and",
    "sample variance",
    "$({s^2})$",
    "To find the",
    "sample mean",
    ", add up the values of all",
    "$4$",
    "samples and divide by",
    "$4$",
    "$ {\\overline{x}} = \\dfrac{\\sum\\limits_{i=1}^{{n}} x_i}{{n}} = \\dfrac{\\sum\\limits_{i=1}^{{4}} x_i}{{4$",
    "To compensate for this underestimation, rather than simply averaging the",
    "squared deviations from the mean",
    ", we total them and divide by",
    "$n - 1$",
    "$ {s^2} = \\dfrac{\\sum\\limits_{i=1}^{{n}} (x_i - {\\overline{x}})^2}{{n - 1}} $",
    "$ {s^2} = \\dfrac{{28.09} + {7.29} + {44.89} + {18.49}} {{4 - 1}} $",
    "$ {s^2} = \\dfrac{{98.76}}{{3}} = {32.92\\text{ years}^2} $",
    "We can estimate that the average meerkat at the zoo is 6.3 years old. There is a variance of 32.92 years $^2$."
  ]
}
{'source': 'AMPS', 'file': 'amps/khan/519/1608137175.json'}