Question

1. the data represents the number of clocks in 9 households: 7, 5, 13, 5, 7, 10, 5, 5, 8. what measure of central tendency best describes the data?

Explanation:

Step1: Identify the data set

The data set is \( 7, 5, 13, 5, 7, 10, 5, 5, 8 \) (note: there are 9 data points, so the last number should be 8 to make 9 values: let's confirm the count: 7,5,13,5,7,10,5,5,8 – that's 9 values).

Step2: Find the mode

The mode is the value that appears most frequently. Let's count the frequency of each number:

• \( 5 \): appears 4 times (positions 2,4,7,8)
• \( 7 \): appears 2 times (positions 1,5)
• \( 13 \): 1 time
• \( 10 \): 1 time
• \( 8 \): 1 time

Step3: Find the median

First, sort the data: \( 5, 5, 5, 5, 7, 7, 8, 10, 13 \). There are 9 values, so the median is the 5th value, which is \( 7 \).

Step4: Find the mean

The mean is calculated as \( \frac{\text{sum of data}}{\text{number of data points}} \).
Sum of data: \( 5 + 5 + 5 + 5 + 7 + 7 + 8 + 10 + 13 = 5 + 5 + 5 + 5 + 7 + 7 + 8 + 10 + 13 \)
Calculate step by step: \( 5\times4 = 20 \), \( 7\times2 = 14 \), then \( 20 + 14 + 8 + 10 + 13 = 20 + 14 = 34; 34 + 8 = 42; 42 + 10 = 52; 52 + 13 = 65 \).
Mean: \( \frac{65}{9} \approx 7.22 \).

Step5: Analyze which measure is best

The data has a mode (5) that appears much more frequently than other values, and there's an outlier? Wait, 13 is a bit higher, but the mode is the most frequent. However, let's check the distribution. The data has multiple 5s, so the mode is a good measure here because it represents the most common number of clocks in households. The mean is affected by the 13? Wait, 13 is not a huge outlier, but the mode is the most frequent. Wait, actually, in data with a clear mode (frequent value), mode is a good measure of central tendency for describing the "typical" value, especially in categorical or discrete data with a dominant frequency. Alternatively, median is robust to outliers, but here the mode is more representative of the most common case. Wait, let's re-examine: the data is \( 5,5,5,5,7,7,8,10,13 \). The mode is 5 (4 times), median 7, mean ~7.22. Since 5 appears most often, the mode best describes the data as it shows the most common number of clocks in households.

Answer:

The mode (which is 5) best describes the data, as it represents the most frequently occurring number of clocks in the households.