Final answer:
Without the individual scores of the 11 students, the standard deviation cannot be calculated. Standard deviation is a measure of the dispersion of a set of values from their mean. The calculation involves finding the mean, subtracting the mean from each score, squaring the deviations, summing them, dividing by the sample size minus one, and taking the square root of this result.
Step-by-step explanation:
To calculate the standard deviation of a sample, you need to know the individual scores of the 11 students. However, from the information provided, we can discuss what standard deviation is and how it might be found given complete data. Standard deviation is a measure of the amount of variation or dispersion in a set of values.
A lower standard deviation means that most of the numbers are close to the mean (average) of the dataset, while a higher standard deviation means that the numbers are more spread out. To calculate it, you would follow these steps:
- Find the mean of the sample by adding all the scores and dividing by the number of scores (in this case, 11).
- Subtract the mean from each score to get the deviation for each score.
- Square each deviation.
- Add all the squared deviations together.
- Divide this total by one less than the number of scores (which is 10 for a sample size of 11, this is because we are using the sample standard deviation formula).
- Take the square root of the result from step 5 to get the standard deviation.
For example, if a sample of 11 students had scores with a mean of 52 and a standard deviation of 11, just as the entrance exam example, their scores follow a normal distribution around that mean with that level of variability. In this hypothetical scenario, if a student had a score of 63, we could say they scored one standard deviation above the mean, since 63 - 52 = 11. Remember, without the actual data, the standard deviation cannot be calculated.