Quizzma Latest Questions

The table below gives the percent of children under five considered to be underweight

Anonymous

The table below gives the percent of children under five considered to be underweight.

Percent of Underweight Children Number of Countries
16.1-21.5 21
21.6-25.9 7
26.0-30.3 7
30.4-35.7 3
35.8-37.3 3
37.4-42.5 3
42.6-48.7 2
  1. What is the best estimate for the mean percentage of underweight children? (Round your answer to two decimal places.)
  2. What is the standard deviation? (Round your answer to two decimal places.)
  3. Which interval(s) could be considered unusual? Explain.
    • None of the intervals could be considered unusual since none of them contain any values in the range of ±2 standard deviations from the mean.
    • The intervals 37.4-42.5 and 42.6-48.7 could be considered unusually high since they contain values that are at least two standard deviations above the mean percentage of underweight children.
    • The interval 26.0-30.3 could be considered unusually high since it contains values that are at least two standard deviations above the mean percentage of underweight children.
    • The interval 16.1-21.5 could be considered unusually low since it contains values that are at least two standard deviations below the mean percentage of underweight children.

 




Related Questions

Leave an answer

Leave an answer

1 Answer

  1. This answer was edited.

    1. Mean Calculation

    To estimate the mean, we’ll use the midpoint for each interval, multiply it by the frequency of that interval, and then sum all the values and divide by the total number of countries.

    Step 1: Find Midpoints

    • For each interval, find the midpoint (average of lower and upper bound).
    Interval Midpoint (x) Frequency (f)
    16.1 – 21.5 18.8 21
    21.6 – 25.9 23.75 7
    26.0 – 30.3 28.15 7
    30.4 – 35.7 33.05 3
    35.8 – 37.3 36.55 3
    37.4 – 42.5 39.95 3
    42.6 – 48.7 45.65 2

    Step 2: Multiply Midpoints by Frequencies

    • Calculate f×xf \times xfor each interval.
    Interval Midpoint (x) Frequency (f) f×xf \times x
    16.1 – 21.5 18.8 21 394.8
    21.6 – 25.9 23.75 7 166.25
    26.0 – 30.3 28.15 7 197.05
    30.4 – 35.7 33.05 3 99.15
    35.8 – 37.3 36.55 3 109.65
    37.4 – 42.5 39.95 3 119.85
    42.6 – 48.7 45.65 2 91.3

    Step 3: Calculate Mean

    • Sum the products f×xf \times xf×x and divide by the total frequency.

    Mean=(f×x)f\text{Mean} = \frac{\sum (f \times x)}{\sum f} Mean=394.8+166.25+197.05+99.15+109.65+119.85+91.321+7+7+3+3+3+2\text{Mean} = \frac{394.8 + 166.25 + 197.05 + 99.15 + 109.65 + 119.85 + 91.3}{21 + 7 + 7 + 3 + 3 + 3 + 2} Mean=1177.054625.59\text{Mean} = \frac{1177.05}{46} \approx 25.59

    2. Standard Deviation Calculation

    Step 1: Calculate (xmean)2(x – \text{mean})^2(xmean)2 for Each Interval

    • Find the deviation of each midpoint from the mean and square it.

    Step 2: Multiply by Frequency

    • Multiply each squared deviation by the frequency for each interval.
    Interval Midpoint (x) (x25.59)2(x – 25.59)^2 Frequency (f) f×(x25.59)2f \times (x – 25.59)^2
    16.1 – 21.5 18.8 46.13 21 968.73
    21.6 – 25.9 23.75 3.38 7 23.66
    26.0 – 30.3 28.15 6.59 7 46.13
    30.4 – 35.7 33.05 55.47 3 166.41
    35.8 – 37.3 36.55 119.71 3 359.13
    37.4 – 42.5 39.95 206.96 3 620.88
    42.6 – 48.7 45.65 403.53 2 807.06

    Step 3: Sum and Divide by Total Frequency

    • Sum the products and divide by the total frequency, then take the square root.

    Variance=(f×(xmean)2)f\text{Variance} = \frac{\sum (f \times (x – \text{mean})^2)}{\sum f} Variance=2992.004665.04\text{Variance} = \frac{2992.00}{46} \approx 65.04 Standard Deviation=65.048.06

    3. Determine Unusual Intervals

    We consider values more than two standard deviations away from the mean to determine if an interval is unusual.

    • Mean = 25.59
    • Standard Deviation = 8.06
    • 2×8.06=16.122 \times 8.06 = 16.12

    Unusual Range:

    • Below: 25.5916.12=9.4725.59 – 16.12 = 9.47
    • Above: 25.59+16.12=41.7125.59 + 16.12 = 41.71

    Unusual Intervals:

    • The interval 42.6 – 48.7 is above 41.71, making it unusually high.

    Conclusion

    • Mean Percentage of Underweight Children: 25.59
    • Standard Deviation: 8.06
    • Unusual Intervals:
      • The intervals 37.4-42.5 and 42.6-48.7 could be considered unusually high since they contain values that are at least two standard deviations above the mean percentage of underweight children.