I need help with (b): A small company with 5 employees wants to know some statistics about their employee's ages. They surveyed the 5 employees and found that their ages were: 22, 29, 35, 37 and 42.
(a)Determine:
Mean age: 33
Median: 35
Range: 20
Variance: 59.5
S.D.: 7.72
(b) How would your answers change if this was a sample of 5 employees from a company of 10,000? I believe it would not change the answers.
Your SD is the sample SD. Your population SD is 6.90.
How does it change if population larger, and sample size stay at 5? Does not change.
To answer question (b), let's consider each statistic one by one:
Mean age: The mean age is calculated by summing up all the ages and dividing by the number of employees. In this case, the mean is 33. If we were to sample 5 employees from a company of 10,000, the mean age would still be calculated in the same way, by summing up the ages of the 5 employees and dividing by 5. The sample size (5) does not affect the overall calculation.
Median: The median is the middle value when the ages are arranged in ascending or descending order. In this case, the median age is 35. If we were to sample 5 employees from a company of 10,000, the process of determining the median would remain the same. The sample size does not influence the calculation of the median.
Range: The range is the difference between the highest and lowest values. In this case, the range is 20. If we were to sample 5 employees from a company of 10,000, the range calculation would still be based on the highest and lowest ages of the sampled employees. The overall company size does not impact the range calculation.
Variance and Standard Deviation (S.D.): Variance measures the spread of data around the mean, and the standard deviation is the square root of the variance. In this case, the variance is 59.5 and the standard deviation is 7.72.
If we were to sample 5 employees from a company of 10,000, the calculation of variance and standard deviation would follow the same formula. The overall size of the company would not affect these statistical values.
In summary, for this particular set of statistics, the answers would not change if the sample was taken from a smaller or larger population. However, it is important to note that when dealing with larger populations, there may be additional considerations when it comes to statistical inference and generalizing the findings to the entire population.