The standard deviation of the amounts saved by Molly using coupons is \(\$2.68\)
Molly's savings data: \(\$\ 6.00, \$\ 9.00, \$\ 3.00, \$\ 9.00, \$\ 3.00\) hence \(n = 5\)
- Find the mean of the savings:
\(\mu = \frac{\Sigma\ x_i}{n}\)
\(\mu = \frac{6 +9 +3 + 9 + 3} {5} = 6\) - Find the variance of the savings:
\(\sigma^2 = \frac{ \Sigma (x_i - \mu)^2}{n}\)
\(\sigma^2 = \frac{ (6 - 6)^2 + (9-6)^2 + (3-6)^2 + (9-6)^2 + (3-6)^2}{5}\)
\(\sigma^2 = \frac{0 + 9 + 9+ 9+ 9}{5} = \frac{36}{5}\) - Calculate the standard deviation:
\(\sigma = \sqrt{\frac{36}{5}}\)
\(\sigma = 2.68\)