of Individuals 140 120 100 60 60 40 20- 160 170 150 190 200 Body Mass (a) 210 220 230

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Below is a distribution of raw scores for Body Mass Index (BMI) for a population. The shape of the "sampling distribution of the mean" where N = 100 for this variable would be which shape?  Hint:  The picture below is not the sampling distribution of mean, but rather the population we use to create a sampling distribution. What shape are sampling distributions of the mean?

Normally distributed.
The shape is impossible to predict.
Skewed in the opposite direction.
Exactly the same.
### Understanding Body Mass Distribution in a Population

This histogram displays the body mass distribution of individuals in a given sample population. The x-axis represents the body mass in grams (g), ranging from 160 g to 230 g. The y-axis represents the number of individuals within each body mass interval.

#### Detailed Analysis:
- The histogram consists of vertical bars, each of which represents a specific range of body mass. The height of each bar indicates the number of individuals within that range.
- The body mass intervals increase in increments of 5 grams, from 160 g to 230 g.
- Most of the data points are concentrated between 160 g and 190 g, suggesting these are the most common body masses within the sample population.

#### Key Observations:
1. **Modal Class**:
   - The tallest bar is centered around the body mass range of 170-175 grams, indicating this is the most frequently occurring body mass range in the sample. Approximately 130 individuals fall into this category.
   
2. **Distribution Shape**:
   - The distribution is right-skewed (positively skewed), meaning there are more individuals with lower body masses and fewer individuals with higher body masses.
   
3. **Range & Spread**:
   - The spread of the data is from 160 g to 230 g, indicating the total range of body masses observed in the population is 70 grams.
   - The left side of the histogram has a steeper ascent compared to the gradual descent on the right side, confirming the right skew.

4. **Frequency Count**:
   - There are fewer than 20 individuals at the extremes of the body mass range (both lower and upper), suggesting that extremely low or high body masses are less common.
   - There is a noticeable decline in the number of individuals as the body mass increases past 190 grams.

This histogram helps in understanding the variability and commonality within the body mass of a population, which can be crucial for studies in health, nutrition, and biology. It is evident that there is a predominant body mass range, but also significant variation outside of that range.
Transcribed Image Text:### Understanding Body Mass Distribution in a Population This histogram displays the body mass distribution of individuals in a given sample population. The x-axis represents the body mass in grams (g), ranging from 160 g to 230 g. The y-axis represents the number of individuals within each body mass interval. #### Detailed Analysis: - The histogram consists of vertical bars, each of which represents a specific range of body mass. The height of each bar indicates the number of individuals within that range. - The body mass intervals increase in increments of 5 grams, from 160 g to 230 g. - Most of the data points are concentrated between 160 g and 190 g, suggesting these are the most common body masses within the sample population. #### Key Observations: 1. **Modal Class**: - The tallest bar is centered around the body mass range of 170-175 grams, indicating this is the most frequently occurring body mass range in the sample. Approximately 130 individuals fall into this category. 2. **Distribution Shape**: - The distribution is right-skewed (positively skewed), meaning there are more individuals with lower body masses and fewer individuals with higher body masses. 3. **Range & Spread**: - The spread of the data is from 160 g to 230 g, indicating the total range of body masses observed in the population is 70 grams. - The left side of the histogram has a steeper ascent compared to the gradual descent on the right side, confirming the right skew. 4. **Frequency Count**: - There are fewer than 20 individuals at the extremes of the body mass range (both lower and upper), suggesting that extremely low or high body masses are less common. - There is a noticeable decline in the number of individuals as the body mass increases past 190 grams. This histogram helps in understanding the variability and commonality within the body mass of a population, which can be crucial for studies in health, nutrition, and biology. It is evident that there is a predominant body mass range, but also significant variation outside of that range.
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