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.
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.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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