Question

a set of data is found to have a sample standard deviation of 28. suppose 5 was added to each of the numbers in the dataset. the standard deviation of the resulting dataset
would be 33.5
would be 14
wouldnt change
cannot be determined from this information

Explanation:

Step1: Recall the property of standard deviation

Standard deviation measures the spread of data. When a constant \(c\) is added to each data point \(x_i\) in a dataset (new data points \(y_i=x_i + c\)), the mean \(\bar{y}=\bar{x}+c\).
The formula for the sample standard deviation is \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}\). For the new data \(y_i=x_i + 5\), the new mean \(\bar{y}=\bar{x}+5\). Then \(y_i-\bar{y}=(x_i + 5)-(\bar{x}+5)=x_i-\bar{x}\).

Step2: Calculate the new standard deviation

The sample standard deviation of the new data \(s_y=\sqrt{\frac{\sum_{i = 1}^{n}(y_i-\bar{y})^2}{n - 1}}=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}\)

Answer:

C. wouldn't change