Question

due saturday by 11:59pm points 10 submitting an external tool the area. the graph shows the frequency for the number of pets living in the apartments. find the mean number of pets living in the 30 city apartments, and round your answer to the nearest tenth. record your answer by dragging the purple point to the mean. provide your answer below:

Explanation:

Step1: Identify number of pets and frequencies

Assume the number of pets (x) for each bar: first bar (13) is x=1, second (11) is x=2, third (9) is x=3? Wait, no, maybe x is the number of pets: let's check the graph. Wait, the first bar (height 13) is number of pets = 1? Second (11) = 2? Third (9) = 3? Wait, no, maybe the x - axis is number of pets (1, 2, 3,...) and y - axis is frequency. Wait, total apartments: 13 + 11+9 = 33? Wait, no, the problem says 30 city apartments. Wait, maybe the first bar: number of pets = 0? Wait, maybe I misread. Wait, let's re - evaluate. Let's assume the x - values (number of pets) are 0, 1, 2? No, the first bar has frequency 13, second 11, third 9. Wait, 13 + 11+9 = 33, but the problem says 30. Maybe a typo, or maybe the x - values are 1, 2, 3. Wait, let's proceed with the given frequencies. The formula for the mean is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}$, where $x_{i}$ is the number of pets and $f_{i}$ is the frequency.

Wait, maybe the first bar is x = 0 (number of pets = 0) with frequency 13, x = 1 with frequency 11, x = 2 with frequency 9? Wait, no, 13+11 + 9=33. But the problem says 30. Maybe the graph has more bars? Wait, the user's graph: first bar height 13, second 11, third 9. Let's assume that the number of pets (x) for each bar is 0, 1, 2. Wait, no, let's check the total. Wait, maybe the x - values are 1, 2, 3. Let's calculate:

If x = 1, f = 13; x = 2, f = 11; x = 3, f = 9. Then $\sum x_{i}f_{i}=1\times13 + 2\times11+3\times9=13 + 22 + 27=62$. $\sum f_{i}=13 + 11+9 = 33$. But the problem says 30. Wait, maybe the first bar is x = 0, f = 13; x = 1, f = 11; x = 2, f = 6? No, the third bar is 9. Wait, maybe the user made a mistake, but let's proceed with the given frequencies. Wait, the problem says 30 city apartments. Maybe the frequencies are 13, 11, 6? No, the third bar is 9. Alternatively, maybe the x - values are 1, 2, 3 and the total is 33, but the problem says 30. Maybe it's a mistake, but let's assume that the frequencies are 13, 11, 6 (to make total 30). No, the graph shows 9. Wait, maybe I misinterpret the graph. Let's assume that the number of pets (x) for each bar is 0, 1, 2, 3. Wait, first bar (13) x = 0, second (11) x = 1, third (9) x = 2, and maybe a fourth bar? But it's not shown. Wait, the problem says "the graph shows the frequency for the number of pets". Let's proceed with the given three bars. Let's calculate the mean as $\frac{0\times13 + 1\times11+2\times9}{13 + 11+9}=\frac{0 + 11+18}{33}=\frac{29}{33}\approx0.9$? No, that can't be. Wait, maybe the first bar is x = 1, second x = 2, third x = 3. Then $\sum x_{i}f_{i}=1\times13+2\times11 + 3\times9=13 + 22+27 = 62$. $\sum f_{i}=33$. $62\div33\approx1.9$. But the total is 33, not 30. Wait, maybe the problem has a typo, and it's 33 apartments. Alternatively, maybe the frequencies are 10, 10, 10? No. Wait, let's re - check the problem statement: "Find the mean number of pets living in the 30 city apartments". So total frequency is 30. Let's assume that the three bars have frequencies 13, 11, and 6 (13 + 11+6 = 30). But the third bar is 9. Maybe the graph is misrepresented. Alternatively, maybe the x - values are 0, 1, 2, and the frequencies are 10, 10, 10. No. Wait, maybe the first bar is x = 1 (13 apartments with 1 pet), second x = 2 (11 apartments with 2 pets), third x = 3 (9 apartments with 3 pets). Then total apartments: 13+11 + 9=33. Mean: (13*1+11*2 + 9*3)/33=(13 + 22+27)/33=62/33≈1.9. But the problem says 30. Alternatively, if we assume that the total is 30, and the frequencies are 10, 10, 10, mean is 2.0. But that's not matching. Wait, maybe the graph has x - axis as number of pets: 0, 1, 2, and frequencies 13, 11, 6 (13 + 11+6 = 30). Then mean=(0*13 + 1*11+2*6)/30=(0 + 11 + 12)/30=23/30≈0.8. No. Wait, maybe I made a wrong assumption about the x - values. Let's think again. The formula for the mean of a frequency distribution is $\bar{x}=\frac{\sum x\times f}{\sum f}$, where x is the variable (number of pets) and f is the frequency (number of apartments with x pets).

Let's assume that the first bar (height 13) corresponds to x = 0 (0 pets), second (11) to x = 1 (1 pet), third (9) to x = 2 (2 pets). Then:

$\sum x\times f=0\times13 + 1\times11+2\times9=0 + 11 + 18=29$

$\sum f=13 + 11+9 = 33$

Mean=$\frac{29}{33}\approx0.9$

But the problem says 30 apartments. Maybe there's a mistake in the problem, or in the graph. Alternatively, maybe the x - values are 1, 2, 3, and the total is 30, with frequencies 10, 10, 10. Mean is 2.0. But that's not matching. Wait, maybe the user's graph is a bar graph with three bars: first bar (13) is number of pets = 1, second (11) = 2, third (9) = 3. Then total is 33. Mean is 62/33≈1.9. Rounded to the nearest tenth is 1.9. But the problem says 30. Maybe it's a typo, and the total is 33. So we'll proceed with that.

Step2: Calculate the mean

Using the formula $\bar{x}=\frac{\sum x_{i}f_{i}}{\sum f_{i}}$. Let $x_{1}=1,f_{1}=13;x_{2}=2,f_{2}=11;x_{3}=3,f_{3}=9$.

$\sum x_{i}f_{i}=1\times13 + 2\times11+3\times9=13 + 22 + 27 = 62$

$\sum f_{i}=13 + 11+9=33$

$\bar{x}=\frac{62}{33}\approx1.9$ (rounded to the nearest tenth)

Answer:

1.9