Household Data 371F89

1. **State the problem:** We have data on the number of people per household collected by Maria: $$3,4,1,2,5,6,7,4,7,8,6,7,2,4,1,3,6,4$$ We need to answer four questions: 3.1 The best way to gather this information. 3.2 Determine the range of the data. 3.3 Calculate the mean. 3.4 Determine the median. 2. **3.1 Best way to gather the information:** The best way to gather data on household sizes is through a **survey or questionnaire** where each household reports the number of people living there. This ensures direct and accurate data collection. 3. **3.2 Determine the range:** - The range is the difference between the maximum and minimum values in the data. - From the data, the minimum value is $1$ and the maximum value is $8$. - So, the range is: $$\text{Range} = 8 - 1 = 7$$ 4. **3.3 Calculate the mean:** - The mean is the sum of all data values divided by the number of data points. - First, count the total number of data points: There are $3$ rows and $6$ columns, so total data points = $3 \times 6 = 18$. - Sum all values: $$3+4+1+2+5+6+7+4+7+8+6+7+2+4+1+3+6+4 = 76$$ - Calculate the mean: $$\text{Mean} = \frac{76}{18} = \frac{\cancel{76}}{\cancel{18}} = 4.22 \text{ (rounded to 2 decimal places)}$$ 5. **3.4 Determine the median:** - The median is the middle value when data is ordered from smallest to largest. - Order the data: $$1,1,2,2,3,3,4,4,4,4,5,6,6,6,6,7,7,7,8$$ - There are $18$ data points (even number), so the median is the average of the 9th and 10th values. - The 9th and 10th values are both $4$. - So, median: $$\text{Median} = \frac{4 + 4}{2} = 4$$ **Final answers:** - 3.1 Best way: Survey or questionnaire. - 3.2 Range: $7$ - 3.3 Mean: $4.22$ - 3.4 Median: $4$