Amy measured her pulse rate while resting, x beats per minute, at the same time each day on 30 days. The results are summarised below.
\(\Sigma (x - 80) = -147\)
\(\Sigma (x - 80)^2 = 952\)
Find the mean and standard deviation of Amy’s pulse rate.
Solution
To find the mean, we use the formula:
\(\bar{x} = 80 - \frac{\Sigma (x - 80)}{30}\)
\(\bar{x} = 80 - \frac{-147}{30} = 80 + 4.9 = 75.1\)
To find the standard deviation, we use the formula:
\(\text{sd} = \sqrt{\frac{\Sigma (x - 80)^2}{30} - \left(\frac{\Sigma (x - 80)}{30}\right)^2}\)
\(\text{sd} = \sqrt{\frac{952}{30} - \left(\frac{-147}{30}\right)^2}\)
\(\text{sd} = \sqrt{31.7333 - 4.9^2} = \sqrt{7.72} \approx 2.78\)
Log in to record attempts.