Final answer:
To find the standard deviation of 10 students' test scores with a sum of 69 and sum of squares 515, calculate the mean and then use the formula for standard deviation of a sample. The calculation yields a standard deviation of approximately 2.08.
Step-by-step explanation:
To calculate the standard deviation of the scores of 10 students in a test, you need to know both the sum of the scores (represented as ΣX) and the sum of the squares of the scores (represented as ΣX2).
From the question, we know that ΣX = 69 and ΣX2 = 515. The standard deviation (σ) for a sample is given by the formula σ = √[(ΣX2 - (ΣX)2/n)/(n-1)], where n is the number of values in the dataset.
Following the steps:
- Calculate the mean (μ) = (ΣX)/n = 69/10 = 6.9.
- Plug the values into the standard deviation formula: σ = √[(515 - (692/10))/(10-1)] = √[(515 - 476.1)/9] = √(38.9/9) = √4.322 = 2.08 (rounded to two decimal places).
The standard deviation of the students' test scores is approximately 2.08.