The table below gives the percent of children under five considered to be underweight.
Percent of Underweight Children Number of Countries
16–21.45 21
21.45–26.9 3
26.9–32.35 9
32.35–37.8 7
37.8–43.25 7
43.25–48.7 2
What is the best estimate for the mean percentage of underweight children? (Round your answer to two decimal places.)
What is the standard deviation? (Round your answer to two decimal places.)
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 plus or minus 2 times standard deviation.
– The intervals 37.25–43.25 and 43.25–48.7 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 43.25–48.7 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 16–21.45 could be considered unusually low since it contains values that are at least two standard deviations below the mean percentage of underweight children.
To find the mean percentage of underweight children and the standard deviation, we’ll first need to set up a calculation based on the data provided.
### Step 1: Calculate the Midpoint for Each Interval
1. 16–21.45: Midpoint = (16 + 21.45) / 2 = 18.725
2. 21.45–26.9: Midpoint = (21.45 + 26.9) / 2 = 24.175
3. 26.9–32.35: Midpoint = (26.9 + 32.35) / 2 = 29.625
4. 32.35–37.8: Midpoint = (32.35 + 37.8) / 2 = 35.075
5. 37.8–43.25: Midpoint = (37.8 + 43.25) / 2 = 40.275
6. 43.25–48.7: Midpoint = (43.25 + 48.7) / 2 = 45.975
### Step 2: Calculate the Mean Percentage
Using the midpoints and number of countries:
– Mean = (Σ(midpoint × number of countries)) / total number of countries
Calculating:
– (18.725 × 21) + (24.175 × 3