Question

the town mayor uses the graph to claim that the town is very pet friendly. part a: find the mean of the data. show or explain each step of work. (2 points) part b: find the median of the data. show or explain each step of work. (1 point) part c: find the mode of the data. show or explain each step of work. (1 point) part d: using your findings in parts a, b, and c, describe the distribution of the data. (1 point)

Explanation:

Step1: Count the frequency of each value

Let's count the number of dots for each number of pets. For 0 pets, there is 1 dot; for 1 pet, 1 dot; for 2 pets, 2 dots; for 3 pets, 2 dots; for 4 pets, 4 dots; for 5 pets, 3 dots; for 6 pets, 2 dots; for 7 pets, 2 dots; for 8 pets, 2 dots; for 9 pets, 1 dot.

Step2: Calculate the sum of the products of values and their frequencies

The sum $S=(0\times1)+(1\times1)+(2\times2)+(3\times2)+(4\times4)+(5\times3)+(6\times2)+(7\times2)+(8\times2)+(9\times1)=0 + 1+4 + 6+16+15+12+14+16+9 =93$. The total number of data - points $n=1 + 1+2+2+4+3+2+2+2+1=20$.

Step3: Calculate the mean

The mean $\bar{x}=\frac{S}{n}=\frac{93}{20}=4.65$.

Step4: Find the median

Arrange the data in ascending order. Since $n = 20$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data values. First, list out all the data values: 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9. The 10th and 11th values are 4 and 5. So the median $M=\frac{4 + 5}{2}=4.5$.

Step5: Find the mode

The mode is the value that appears most frequently. The value 4 appears 4 times, more frequently than any other value, so the mode $Mo = 4$.

Step6: Describe the distribution

The mean ($4.65$), median ($4.5$) and mode ($4$) are relatively close. The distribution is approximately symmetric or slightly right - skewed since the mean is slightly larger than the median.

Answer:

Part A: The mean of the data is 4.65.
Part B: The median of the data is 4.5.
Part C: The mode of the data is 4.
Part D: The distribution is approximately symmetric or slightly right - skewed since the mean is slightly larger than the median, and the mean, median and mode are relatively close.