Question

based on the following calculator output, determine the sample standard deviation of the dataset, rounding to the nearest tenth if necessary:
1-var-stats
(\bar{x} = 201)
(sum x = 4221)
(sum x^2 = 850555)
(s_x = 10.329569206893384)
(sigma_x = 10.080627342534175)
(n = 21)
(\text{min}x = 183)
(q_1 = 192)
(\text{med} = 202)
(q_3 = 208.5)
(\text{max}x = 220)

Explanation:

Step1: Recall Sample Std Dev Formula

The formula for sample standard deviation \( s \) is \( s = \sqrt{\frac{\sum x^2 - \frac{(\sum x)^2}{n}}{n - 1}} \), or we can use the given \( Sx \) (sample standard deviation) from the output.

Step2: Identify the Sample Std Dev

From the calculator output, \( Sx = 10.329569206893384 \). Rounding to the nearest tenth (one decimal place), we look at the hundredth place: 2 (since 10.329... has hundredth digit 2). Since 2 < 5, we round down.

Answer:

10.3