Question

russell has surveyed their 30 classmates about the number of pets in their household and received the following data: 6 1 2 1 3 5 4 2 4 3 1 5 1 2 1 2 1 5 2 6 1 6 6 0 0 4 2 3 4 2 construct a frequency and relative frequency distribution table: (round the relative frequencies to 4 decimal places) number of pets frequency relative frequency 0 2 1 7 2 7 3 3 4 4 5 3 6 4 total: question help: video written example

Explanation:

Step1: Recall relative - frequency formula

The formula for relative frequency is $\text{Relative Frequency}=\frac{\text{Frequency}}{\text{Total Frequency}}$. The total number of data points is $n = 30$ (since 30 classmates were surveyed).

Step2: Calculate relative frequency for 0 pets

For the number of pets $x = 0$, the frequency $f_0=2$. The relative frequency $rf_0=\frac{2}{30}\approx0.0667$.

Step3: Calculate relative frequency for 1 pet

For $x = 1$, the frequency $f_1 = 7$. The relative frequency $rf_1=\frac{7}{30}\approx0.2333$.

Step4: Calculate relative frequency for 2 pets

For $x = 2$, the frequency $f_2 = 7$. The relative frequency $rf_2=\frac{7}{30}\approx0.2333$.

Step5: Calculate relative frequency for 3 pets

For $x = 3$, the frequency $f_3 = 3$. The relative frequency $rf_3=\frac{3}{30}=0.1000$.

Step6: Calculate relative frequency for 4 pets

For $x = 4$, the frequency $f_4 = 4$. The relative frequency $rf_4=\frac{4}{30}\approx0.1333$.

Step7: Calculate relative frequency for 5 pets

For $x = 5$, the frequency $f_5 = 3$. The relative frequency $rf_5=\frac{3}{30}=0.1000$.

Step8: Calculate relative frequency for 6 pets

For $x = 6$, the frequency $f_6 = 4$. The relative frequency $rf_6=\frac{4}{30}\approx0.1333$.

Step9: Calculate total frequency

The total frequency is the sum of all individual frequencies. $2 + 7+7 + 3+4 + 3+4=30$. The total relative - frequency is always 1.0000 (since $\sum_{i}\frac{f_i}{n}=\frac{\sum_{i}f_i}{n}$, and $\sum_{i}f_i=n$).

Answer:

Number of pets	Frequency	Relative Frequency
1	7	0.2333
2	7	0.2333
3	3	0.1000
4	4	0.1333
5	3	0.1000
6	4	0.1333
Total:	30	1.0000