Alice has measured the hemoglobin levels of 200 people. If the data follows a normal distribution with a mean of 10 and a standard deviation of 1, what can you conclude?
Among several other possible conclusions, you can say that about 2/3 of the 200 will be between 9 and 11, and about 95% will be between 8 and 12.
To draw conclusions about the hemoglobin levels, we need to examine the given information and apply statistical concepts. In this case, we are provided with the following information:
- The data follows a normal distribution.
- The mean (also referred to as the average) of the data is 10.
- The standard deviation (SD) is 1.
Based on this information, we can make the following conclusions:
1. Central Tendency: The mean (average) hemoglobin level for the 200 people is 10. This suggests that, on average, the hemoglobin level is around 10.
2. Spread or Dispersion: The standard deviation (SD) of 1 indicates how much the individual hemoglobin values tend to deviate from the mean. A smaller standard deviation suggests less variability or dispersion in the data. In this case, a standard deviation of 1 suggests that most of the hemoglobin values are close to the mean of 10.
3. Normal Distribution: Since the data follows a normal distribution, we can use the properties of a normal distribution to make further conclusions. For example:
a. Approximate Percentiles: Knowing that the data is normally distributed, we can estimate the percentage of people with hemoglobin levels within specific ranges. For instance, about 68% of the individuals (approximately one standard deviation on either side of the mean) would have hemoglobin levels between 9 and 11.
b. Outliers: Extreme values that deviate significantly from the mean might be considered outliers. Using the normal distribution properties, we can identify and investigate if any values fall outside a certain range. However, since no specific range is provided, we cannot determine if there are any outliers in this case.
4. Sample Size: The fact that 200 people were measured indicates a relatively large sample size. With a larger sample size, our conclusions and estimates are generally more reliable and representative of the larger population.
It's important to note that these conclusions are specific to the information provided. Additional analyses or specific research questions may require further statistical tests or considerations.