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The heights of a group of boys and girls at a local middle school are shown on the dot plots below.

2 dot plots with number lines going from 40 to 60. A plot is titled Boy's Heights. There are 0 dots above 40, 1 above 41, 3 above 44, 3 above 46, 2 above 48, 3 above 50, 4 above 52, 4 above 54, and 0 above 56, 58, and 60. A plot is titled Girl's Heights. There are 0 dots above 40 and 41, 2 dots above 44, 3 above 46, 1 above 48, 3 above 50, 4 above 52, 3 above 54, 4 above 56, and 0 above 58 and 60.

When comparing the shapes of the two sets of data, what conclusion can someone draw?
The shortest boy is taller than the shortest girl.
The range for the girls is greater than the range for the boys.
There is an outlier in the data for the boys, but not for the girls.
The girls are generally taller than the boys.

1 answer

To analyze the information provided about the heights of boys and girls, let’s summarize the data:

Boys' Heights:

  • 0 dots at 40 and 41
  • 1 dot at 41
  • 3 dots at 44
  • 3 dots at 46
  • 2 dots at 48
  • 3 dots at 50
  • 4 dots at 52
  • 4 dots at 54
  • 0 dots at 56, 58, and 60

This indicates the lowest height for boys is 41.

Girls' Heights:

  • 0 dots at 40 and 41
  • 2 dots at 44
  • 3 dots at 46
  • 1 dot at 48
  • 3 dots at 50
  • 4 dots at 52
  • 3 dots at 54
  • 4 dots at 56
  • 0 dots at 58 and 60

This indicates the lowest height for girls is 44.

Now analyzing the provided conclusions:

  1. The shortest boy is taller than the shortest girl.

    • True, as the shortest boy (41) is indeed taller than the shortest girl (44).

  2. The range for the girls is greater than the range for the boys.

    • Range for boys: Highest (54) - Lowest (41) = 13.
    • Range for girls: Highest (56) - Lowest (44) = 12.
    • This statement is false because the range for boys is actually greater.

  3. There is an outlier in the data for the boys but not for the girls.

    • An outlier is a value that is significantly higher or lower than the others. There doesn't appear to be an outlier in boys' heights, as the values are relatively clustered. This statement is false.

  4. The girls are generally taller than the boys.

    • This seems incorrect based on the average height values. The graphs imply there are many boys in the lower height ranges, while the girls are clustered slightly higher.

Based on this analysis, the most accurate conclusion is:

The shortest boy is taller than the shortest girl.