\begin{tabular}{|l|l|}\hline & \\ \hline 2. Find the mean: & \( \begin{array}{l}\text { 5. Find the }\end{array} \) \\ \( 23,91,83,31,49,11,60,92 \) & \( \begin{array}{l}68,40,39 \\ 32,69,78\end{array} \) \\ \hline\end{tabular}

To find the mean of the given sets of numbers, we will follow these steps: 1. **Calculate the sum of the numbers.** 2. **Count the number of values.** 3. **Divide the sum by the count to find the mean.** ### Step 1: Calculate the Mean of the First Set The first set of numbers is: \( 23, 91, 83, 31, 49, 11, 60, 92 \). **Sum of the numbers:** \[ S_1 = 23 + 91 + 83 + 31 + 49 + 11 + 60 + 92 \] ### Step 2: Count the Number of Values There are 8 values in the first set. ### Step 3: Calculate the Mean The mean \( M_1 \) is calculated as: \[ M_1 = \frac{S_1}{8} \] ### Step 4: Calculate the Mean of the Second Set The second set of numbers is: \( 68, 40, 39, 32, 69, 78 \). **Sum of the numbers:** \[ S_2 = 68 + 40 + 39 + 32 + 69 + 78 \] ### Step 5: Count the Number of Values There are 6 values in the second set. ### Step 6: Calculate the Mean The mean \( M_2 \) is calculated as: \[ M_2 = \frac{S_2}{6} \] Now, let's perform the calculations for both sets. #### Calculating \( S_1 \) and \( M_1 \): \[ S_1 = 23 + 91 + 83 + 31 + 49 + 11 + 60 + 92 \] #### Calculating \( S_2 \) and \( M_2 \): \[ S_2 = 68 + 40 + 39 + 32 + 69 + 78 \] Let's compute these sums and means. Calculate the value by following steps: - step0: Calculate: \(23+91+83+31+49+11+60+92\) - step1: Add the numbers: \(440\) Calculate or simplify the expression \( 68 + 40 + 39 + 32 + 69 + 78 \). Calculate the value by following steps: - step0: Calculate: \(68+40+39+32+69+78\) - step1: Add the numbers: \(326\) Calculate or simplify the expression \( 440 / 8 \). Calculate the value by following steps: - step0: Calculate: \(\frac{440}{8}\) - step1: Reduce the numbers: \(\frac{55}{1}\) - step2: Calculate: \(55\) Calculate or simplify the expression \( 326 / 6 \). Calculate the value by following steps: - step0: Calculate: \(\frac{326}{6}\) - step1: Reduce the fraction: \(\frac{163}{3}\) ### Results 1. **Mean of the First Set:** - The sum \( S_1 \) of the first set \( 23, 91, 83, 31, 49, 11, 60, 92 \) is \( 440 \). - The mean \( M_1 \) is calculated as: \[ M_1 = \frac{440}{8} = 55 \] 2. **Mean of the Second Set:** - The sum \( S_2 \) of the second set \( 68, 40, 39, 32, 69, 78 \) is \( 326 \). - The mean \( M_2 \) is calculated as: \[ M_2 = \frac{326}{6} = \frac{163}{3} \approx 54.33 \text{ or } 54\frac{1}{3} \] ### Final Answers - The mean of the first set is \( 55 \). - The mean of the second set is \( \frac{163}{3} \) or approximately \( 54.33 \).