Question

rachel has surveyed their 25 classmates about the number of cars in their household and received the following data:
5 0 5 2 2
5 5 3 4 4
0 5 0 3 2
6 4 2 1 1
0 2 2 6 6
construct a frequency and relative frequency distribution table (round relative frequencies to 2 decimal places)
number of cars frequency relative frequency
0
1
2
3
4
5
6
total:
construct a histogram:

Explanation:

Step1: Count frequency of 0

Count the number of 0s in the data set. There are 4 zeros. So frequency of 0 is 4.

Step2: Calculate relative - frequency of 0

Relative frequency = $\frac{\text{Frequency}}{\text{Total number of data points}}$. Total number of data points is 25. So relative frequency of 0 is $\frac{4}{25}=0.16$.

Step3: Count frequency of 1

Count the number of 1s in the data set. There are 2 ones. So frequency of 1 is 2.

Step4: Calculate relative - frequency of 1

Relative frequency of 1 is $\frac{2}{25}=0.08$.

Step5: Count frequency of 2

Count the number of 2s in the data set. There are 7 twos. So frequency of 2 is 7.

Step6: Calculate relative - frequency of 2

Relative frequency of 2 is $\frac{7}{25}=0.28$.

Step7: Count frequency of 3

Count the number of 3s in the data set. There are 2 threes. So frequency of 3 is 2.

Step8: Calculate relative - frequency of 3

Relative frequency of 3 is $\frac{2}{25}=0.08$.

Step9: Count frequency of 4

Count the number of 4s in the data set. There are 3 fours. So frequency of 4 is 3.

Step10: Calculate relative - frequency of 4

Relative frequency of 4 is $\frac{3}{25}=0.12$.

Step11: Count frequency of 5

Count the number of 5s in the data set. There are 4 fives. So frequency of 5 is 4.

Step12: Calculate relative - frequency of 5

Relative frequency of 5 is $\frac{4}{25}=0.16$.

Step13: Count frequency of 6

Count the number of 6s in the data set. There are 3 sixes. So frequency of 6 is 3.

Step14: Calculate relative - frequency of 6

Relative frequency of 6 is $\frac{3}{25}=0.12$.

Step15: Calculate total frequency

Total frequency is the sum of all frequencies, which is $4 + 2+7 + 2+3 + 4+3=25$.

Step16: Calculate total relative - frequency

Total relative - frequency is the sum of all relative frequencies, which is $0.16+0.08 + 0.28+0.08+0.12+0.16+0.12 = 1$.

Answer:

Number of cars	Frequency	Relative Frequency
1	2	0.08
2	7	0.28
3	2	0.08
4	3	0.12
5	4	0.16
6	3	0.12
Total	25	1