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Answer :
To decide whether the statement is true or false, we need to understand a bit about how heights are typically distributed. Human heights tend to follow a normal distribution, which is a bell-shaped distribution where most people's heights are around the average, with fewer people being much taller or much shorter.
In a normal distribution:
1. The mean (average) is the center point.
2. Most data points are clustered around this mean, and the distribution is symmetric.
3. Standard deviation is a measure that indicates the spread of the data points.
We are asked to consider the number of boys in two height ranges: 158-163 cm and 163-167 cm.
Here’s how we can think about it:
- Symmetry of Normal Distribution: If the mean height is around 163 cm, the number of boys from 158 to 163 cm should be approximately equal to the number of boys from 163 to 167 cm, because these ranges are equally distant from 163 cm in a typical symmetric distribution.
- Equal Ranges: Since both ranges (158-163 cm and 163-167 cm) are of equal width (5 cm), and assuming a normal distribution with a symmetrical bell curve, the number of individuals in each range should be nearly equal.
Without specific data but considering these characteristics of normal distribution, it is reasonable to conclude that there are approximately as many boys between 158 and 163 cm as there are between 163 and 167 cm.
Therefore, the statement is True.
In a normal distribution:
1. The mean (average) is the center point.
2. Most data points are clustered around this mean, and the distribution is symmetric.
3. Standard deviation is a measure that indicates the spread of the data points.
We are asked to consider the number of boys in two height ranges: 158-163 cm and 163-167 cm.
Here’s how we can think about it:
- Symmetry of Normal Distribution: If the mean height is around 163 cm, the number of boys from 158 to 163 cm should be approximately equal to the number of boys from 163 to 167 cm, because these ranges are equally distant from 163 cm in a typical symmetric distribution.
- Equal Ranges: Since both ranges (158-163 cm and 163-167 cm) are of equal width (5 cm), and assuming a normal distribution with a symmetrical bell curve, the number of individuals in each range should be nearly equal.
Without specific data but considering these characteristics of normal distribution, it is reasonable to conclude that there are approximately as many boys between 158 and 163 cm as there are between 163 and 167 cm.
Therefore, the statement is True.
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