Alright class, let's tackle each question step-by-step to fully understand the data from the survey:
### Given Data:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Number of People} & \text{Frequency} \\
\hline
1 & 22 \\
\hline
2 & 10 \\
\hline
3 & 5 \\
\hline
4 & 1 \\
\hline
5 & 1 \\
\hline
6 & 2 \\
\hline
7 & 6 \\
\hline
\end{array}
\][/tex]
### Part (a) How many cars were included in the survey?
- To find the total number of cars, we sum the frequencies (how often each number of people were counted).
- Total cars = 22 + 10 + 5 + 1 + 1 + 2 + 6 = 47 cars
### Part (b) How many people travelling by car were counted in the survey?
- To find the total number of people, we need to calculate the sum of the product of the number of people and their respective frequencies.
- Total people = (1 22) + (2 10) + (3 5) + (4 1) + (5 1) + (6 2) + (7 * 6) = 22 + 20 + 15 + 4 + 5 + 12 + 42 = 120 people
### Part (c) Calculate the mean number of people in each car.
- The mean is the total number of people divided by the total number of cars.
- Mean number of people per car = Total people / Total cars = 120 / 47 ≈ 2.55 people per car
### Part (d) Calculate the median number of people in each car.
- To find the median, we need to list all data points in ascending order:
- Frequency of 1: 22 cars
- Frequency of 2: 10 cars
- Frequency of 3: 5 cars
- Frequency of 4: 1 car
- Frequency of 5: 1 car
- Frequency of 6: 2 cars
- Frequency of 7: 6 cars
- When sorted: [1, 1, 1, ..., 1 (22 times), 2, 2, ..., 2 (10 times), 3, 3, ..., 3 (5 times), 4, 5, 6, 6, 7, 7, ..., 7 (6 times)]
- The total number of data points is 47, an odd number, so the median is the 24th value in this ordered list, which falls into the range of 2's.
- Median number of people per car = 2
### Part (e)
#### (i) What is the greatest number of people counted in a car?
- The highest number in our table is 7.
- Greatest number of people = 7 people
#### (ii) What is the smallest number of people counted in a car?
- The lowest number in our table is 1.
- Smallest number of people = 1 person
#### (iii) Calculate the range of the numbers of people travelling in a car.
- The range is the difference between the greatest and smallest numbers.
- Range = Greatest number - Smallest number = 7 - 1 = 6
### Summary:
- Total cars: 47 cars
- Total people: 120 people
- Mean number of people per car: 2.55 people per car
- Median number of people per car: 2
- Greatest number of people in a car: 7 people
- Smallest number of people in a car: 1 person
- Range of the number of people in a car: 6
I hope this step-by-step breakdown clarifies the process for you all!
