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The table below gives the percent of children under five considered to be underweight.Percent of Underweight Children Number of Countries16–21.45 2121.45–26.9 526.9–32.35 1132.35–37.8 637.8–43.25 743.25–48.7 1What is the best estimate for the mean percentage of underweight children? (Round your answer to two decimal places.)

Question

The table below gives the percent of children under five considered to be underweight.Percent of Underweight Children Number of Countries16–21.45 2121.45–26.9 526.9–32.35 1132.35–37.8 637.8–43.25 743.25–48.7 1What is the best estimate for the mean percentage of underweight children? (Round your answer to two decimal places.)

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Solution

To estimate the mean percentage of underweight children, we need to find the midpoint of each range, multiply it by the number of countries in that range, sum up these products, and then divide by the total number of countries.

  1. First, find the midpoint of each range:

    • 16–21.45: (16 + 21.45) / 2 = 18.725
    • 21.45–26.9: (21.45 + 26.9) / 2 = 24.175
    • 26.9–32.35: (26.9 + 32.35) / 2 = 29.625
    • 32.35–37.8: (32.35 + 37.8) / 2 = 35.075
    • 37.8–43.25: (37.8 + 43.25) / 2 = 40.525
    • 43.25–48.7: (43.25 + 48.7) / 2 = 45.975
  2. Multiply each midpoint by the number of countries in that range:

    • 18.725 * 2 = 37.45
    • 24.175 * 5 = 120.875
    • 29.625 * 11 = 325.875
    • 35.075 * 6 = 210.45
    • 40.525 * 7 = 283.675
    • 45.975 * 1 = 45.975
  3. Sum up these products: 37.45 + 120.875 + 325.875 + 210.45 + 283.675 + 45.975 = 1024.3

  4. Divide this sum by the total number of countries: 1024.3 / 32 = 32.009375

So, the best estimate for the mean percentage of underweight children is approximately 32.01% (rounded to two decimal places).

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