Sure! Let's work through each part of this problem step by step.
### Question 4: Calculate the mean number of people per household.
The mean (or average) is calculated by summing all the values and then dividing by the count of values.
We have the dataset: [tex]\( \{1, 6, 2, 4, 4, 3, 5, 5, 2, 8\} \)[/tex].
Step-by-Step Calculation:
1. Sum of the numbers:
[tex]\[
1 + 6 + 2 + 4 + 4 + 3 + 5 + 5 + 2 + 8 = 40
\][/tex]
2. Number of data points:
[tex]\[
10
\][/tex]
3. Mean:
[tex]\[
\frac{40}{10} = 4.0
\][/tex]
### Answer:
The mean number of people per household is 4.0.
### Question 5: Calculate the MAD (Median Absolute Deviation) of the number of people per household.
MAD is calculated as the median of the absolute deviations from the median of the data.
Step-by-Step Calculation:
1. Find the median of the dataset.
- Ordered dataset: [tex]\( \{1, 2, 2, 3, 4, 4, 5, 5, 6, 8\} \)[/tex]
- As we have an even number of elements, the median will be the average of the 5th and 6th values:
[tex]\[
\text{Median} = \frac{4 + 4}{2} = 4.0
\][/tex]
2. Calculate the absolute deviations from the median:
[tex]\[
|1-4|, |6-4|, |2-4|, |4-4|, |4-4|, |3-4|, |5-4|, |5-4|, |2-4|, |8-4| = 3, 2, 2, 0, 0, 1, 1, 1, 2, 4
\][/tex]
3. Ordered absolute deviations:
[tex]\[
\{0, 0, 1, 1, 1, 2, 2, 2, 3, 4\}
\][/tex]
4. Find the median of these absolute deviations:
- Since there are 10 absolute deviations, the median will again be the average of the 5th and 6th values:
[tex]\[
\text{MAD} = \frac{1 + 2}{2} = 1.5
\][/tex]
### Answer:
The MAD of the number of people per household is 1.5.
### Question 6: Conclusions about the "typical" number of people in each household
By examining the mean and considering the MAD:
1. Mean: The mean number of people per household is 4.0. This is a measure of central tendency and suggests that on average, there are 4 people in each household.
2. MAD: The MAD is 1.5, indicating that the number of people in households typically deviates by about 1.5 people from the median household size. This is a measure of how spread out the values are from the median.
### Conclusion:
The "typical" number of people per household in Frank's town can be considered around 4. The mean of 4.0 suggests that, on average, households contain 4 people. The relatively low MAD of 1.5 implies that most households have a size not too far from this average, meaning there are moderate variations around this number, but it is a fair representation of a "typical" household size.
