Question

daphne is examining the alcohol consumed by american men. she collects data from 15 men under 40 with the data in ounces below. find the standard deviation for this set, using the ti - 84. round to 3 decimal places if necessary. 20 30 31 18 25 17 2 6 20 29 9 8 13 24 13 provide your answer below: standard deviation = \square

Explanation:

Step1: Enter data into TI - 84

First, we need to enter the data set \(\{2, 6, 8, 9, 13, 13, 17, 18, 20, 20, 24, 25, 29, 30, 31\}\) (we first sort the data for clarity, but the process on TI - 84 is to enter the raw data: \(20, 30, 31, 18, 25, 17, 2, 6, 20, 29, 9, 8, 13, 24, 13\)) into the list editor of the TI - 84. To do this, we press STAT then EDIT and enter the data into L1.

Step2: Calculate standard deviation

After entering the data, we press STAT again, then move to the CALC menu. We select 1 - Var Stats and press ENTER. The TI - 84 will then display the statistics for the data set. The sample standard deviation (since we have a sample of 15 men) is denoted by \(s\).

When we calculate the 1 - variable statistics for the data set:

• First, we find the mean \(\bar{x}=\frac{2 + 6+8 + 9+13+13+17+18+20+20+24+25+29+30+31}{15}=\frac{265}{15}\approx17.6667\)
• Then, we calculate the sum of squared deviations \(\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}\)
• For example, for \(x_1 = 2\), \((2 - 17.6667)^{2}=( - 15.6667)^{2}\approx245.444\)
• For \(x_2=6\), \((6 - 17.6667)^{2}=( - 11.6667)^{2}\approx136.111\)
• And so on for all 15 data points. Then we sum these squared deviations and divide by \(n - 1=14\) and take the square root.

Using the TI - 84, when we run 1 - Var Stats on the data set, we get \(s\approx9.232\) (after rounding to three decimal places).

Answer:

\(9.232\)