IF A PERSON SCORE 16% HIGHER Than population what is standard deviation?
Did they give you any additional info? I'm not sure this is enough information to calculate the standard deviation.
using a z-score table
16% above the mean of a population is approximately .7 s.d.
To calculate the standard deviation, you need more information than just the percentage by which a person's score is higher than the population. The standard deviation measures the dispersion or spread of a dataset, so at the very least, you would need the individual's score and the scores of the population.
If you have the individual's score and the population scores, you can use the following steps to calculate the standard deviation:
1. Calculate the mean (average) of the population scores.
2. Subtract the mean from each individual score to obtain the deviations.
3. Square each deviation.
4. Calculate the mean of the squared deviations.
5. Take the square root of the mean squared deviation to obtain the standard deviation.
Without specific data, it is not possible to calculate the standard deviation in this case.
To determine the standard deviation when a person scores 16% higher than the population, we need more information. The standard deviation measures the spread or dispersion of data points from the mean (average) of a population or sample.
To calculate the standard deviation, you typically need a set of data points, not just the fact that someone scored higher. However, if you have access to the entire population's data, you can use the following steps to calculate the standard deviation:
1. Determine the average (mean) score of the population.
2. Calculate the difference between each individual score and the mean.
3. Square each difference found in step 2.
4. Sum up all the squared differences.
5. Divide the sum of squared differences by the total number of scores in the population.
6. Take the square root of the result obtained in step 5.
Let's say the average score of the population is 60. To calculate the standard deviation, follow these steps:
1. Determine the average score: 60.
2. Calculate the difference between each individual score and the mean.
- For example, if a person scored 16% higher, their score would be 60 + 0.16 * 60 = 69.6 (approximately 69.6).
- Calculate the difference: 69.6 - 60 = 9.6.
3. Square the difference: (9.6)^2 = 92.16.
4. Sum up all the squared differences.
- If you have access to the entire population's data, sum up all such squared differences.
5. Divide the sum of squared differences by the total number of scores in the population.
- Again, if you have access to the entire population's data, divide the sum by the total number of scores.
6. Take the square root of the result obtained in step 5.
- Calculate the square root of the above result to find the standard deviation.
Note that this calculation assumes that the population's distribution follows a normal distribution. If the distribution is different (e.g., skewed), additional methods may be required to estimate the standard deviation.