Certainly! Let's address each part of this problem step-by-step.
### Part (a): Finding the Modal Number of Bedrooms
The modal average, or mode, is the value that appears most frequently in a data set.
1. First, observe the "Frequency" column to determine which number of bedrooms appears most frequently.
2. From the table, we have:
- 1 bedroom: 5 houses
- 2 bedrooms: 10 houses
- 3 bedrooms: 15 houses
- 4 bedrooms: 7 houses
- 5 bedrooms: 3 houses
3. The frequency of 3 bedrooms (15 houses) is the highest.
Therefore, the modal (most common) number of bedrooms is 3.
### Part (b): Working Out the Mean Number of Bedrooms
The mean number of bedrooms is calculated by taking the total number of bedrooms across all houses and dividing it by the total number of houses.
1. List the data for better understanding:
- Number of houses with 1 bedroom: 5
- Number of houses with 2 bedrooms: 10
- Number of houses with 3 bedrooms: 15
- Number of houses with 4 bedrooms: 7
- Number of houses with 5 bedrooms: 3
2. Calculate the total number of bedrooms:
[tex]\[
(1 \times 5) + (2 \times 10) + (3 \times 15) + (4 \times 7) + (5 \times 3)
\][/tex]
[tex]\[
= 5 + 20 + 45 + 28 + 15
\][/tex]
[tex]\[
= 113
\][/tex]
3. Calculate the total number of houses:
[tex]\[
5 + 10 + 15 + 7 + 3 = 40
\][/tex]
4. Now, compute the mean number of bedrooms:
[tex]\[
\text{Mean} = \frac{\text{Total number of bedrooms}}{\text{Total number of houses}}
\][/tex]
[tex]\[
\text{Mean} = \frac{113}{40}
\][/tex]
[tex]\[
\text{Mean} = 2.825
\][/tex]
Thus, the mean number of bedrooms is approximately 2.825.
### Summary:
- The modal number of bedrooms is 3.
- The mean number of bedrooms is approximately 2.825.
