Question: Find the mean, median, and mode. Annual Household Income \[ \begin{array}{c|c} \text{Stem} &…

Find the mean, median, and mode.

Annual Household Income

\[ \begin{array}{c|c} \text{Stem} & \text{Leaf} \\ \hline 0 & 7 \, 9 \, 9 \\ 1 & 3 \, 3 \, 4 \, 6 \, 9 \\ 2 & 6 \, 7 \\ 3 & 5 \\ \end{array} \]

Key: \(1|3 = 13,000\)

A) Mode = 10,000 and 18,000, Median = 15,000 and Mean = 15,909.09

B) Mode = 11,000, Median = 14,000 and Mean = 18,363.64

C) Mode = 27,000, Median = 22,000 and Mean = 20,818.18

D) Mode = 9,000 and 13,000, Median = 14,000 and Mean = 17,090.91

Solution

First, translate the stem-and-leaf plot into actual numbers: - Stem 0: 7, 9, 9 → 7,000; 9,000; 9,000 - Stem 1: 3, 3, 4, 6, 9 → 13,000; 13,000; 14,000; 16,000; 19,000 - Stem 2: 6, 7 → 26,000; 27,000 - Stem 3: 5 → 35,000 The data set is: 7,000; 9,000; 9,000; 13,000; 13,000; 14,000; 16,000; 19,000; 26,000; 27,000; 35,000 Find the mode: The mode is the number that appears most frequently. The mode values are 9,000 and 13,000. Find the median: Arrange the numbers in ascending order (already done above). The median is the middle number. Here, it is the 6th number in a sorted list of 11 numbers. The median is 14,000. Find the mean: Add all the numbers together and divide by the number of elements. \[ \text{Mean} = \frac{7,000 + 9,000 + 9,000 + 13,000 + 13,000 + 14,000 + 16,000 + 19,000 + 26,000 + 27,000 + 35,000}{11} \] \[ \text{Mean} = \frac{188,000}{11} = 17,090.91 \] Thus, the correct answer is: Mode = 9,000 and 13,000, Median = 14,000, Mean = 17,090.91 (Option D).