Name Gender Age Category
A Female 48 adults
B Male 50 adults
C Female 75 seniors
D Male 1 babies
E Male 25 young adults
F Female 5 children
G Male 14 teen
H Female 16 teen
I Male 7 children
1. For the data above, calculate the following statistic values.
• Mean, median, mode age and percentiles of 25%, 50%, and 75% for all data.
2. Answer the probability questions below
• What is the probability that you will choose a person in the young adults or adults category?
• What is the probability of you choosing a person from the teens category, and then, without replacing the name, choosing someone from the children category?
• What is the probability of you choosing a person from the young adults or adults category, and then, after replacing the name, choosing someone from the children category?
• A driver comes to pick up members of your family for a family reunion. The van holds 7 people, not including the driver. Assuming that none of the babies will be riding in the van, how many different ways can 7 people be chosen to ride in the van?
To answer the questions, we will need to perform some calculations and apply probability concepts. Let's go step by step.
1. To calculate the statistic values, we can follow these steps:
- Find the mean: Add up all the ages and divide by the total number of people.
- Find the median: Arrange the ages in ascending order and find the middle value. If there is an even number of data points, take the average of the two middle values.
- Find the mode: Identify the age that appears most frequently.
- Find the percentiles: Arrange the ages in ascending order and find the age that divides the data into the desired percentage on either side.
Let's calculate these values for the given data:
Mean age:
(48 + 50 + 75 + 1 + 25 + 5 + 14 + 16 + 7) / 9 = 241 / 9 ≈ 26.78
Median age:
Arrange the ages in ascending order: 1, 5, 7, 14, 16, 25, 48, 50, 75.
Median age is the middle value: 16.
Mode age:
No age appears more than once, so there is no mode.
Percentiles:
Arrange the ages in ascending order: 1, 5, 7, 14, 16, 25, 48, 50, 75.
- 25th percentile: Divides the lower 25% and upper 75%. The age at (0.25 * (n + 1))th position = (0.25 * (9 + 1))th position = 0.25 * 10 = 2.5. Since it's not an integer, we take the average of the values at positions 2 and 3: (5 + 7) / 2 = 6.
- 50th percentile (median): Already calculated as 16.
- 75th percentile: Divides the lower 75% and upper 25%. The age at (0.75 * (n + 1))th position = (0.75 * (9 + 1))th position = 0.75 * 10 = 7.5. Since it's not an integer, we take the average of the values at positions 7 and 8: (48 + 50) / 2 = 49.
Thus, the statistic values are:
Mean age ≈ 26.78
Median age = 16
Mode age = None
25th percentile = 6
50th percentile = 16
75th percentile = 49
2. Probability questions:
To answer the probability questions, we need to know the total number of people in each category.
- What is the probability that you will choose a person in the young adults or adults category?
The young adults and adults category consists of A, B, and E. The total number of people in this category = 3.
Probability = Number of people in the category / Total number of people = 3 / 9 = 1/3 ≈ 0.333
- What is the probability of you choosing a person from the teens category and then, without replacing the name, choosing someone from the children category?
The teens category consists of G and H, and the children category consists of F and I. The total number of people in the teens category = 2, and the total number of people in the children category = 2.
Probability = (Number of people in the teens category / Total number of people) * (Number of people in the children category / (Total number of people - 1))
= (2 / 9) * (2 / 8) ≈ 0.0556
- What is the probability of you choosing a person from the young adults or adults category and then, after replacing the name, choosing someone from the children category?
Probability = (Number of people in the young adults or adults category / Total number of people) * (Number of people in the children category / Total number of people)
= (3 / 9) * (2 / 9) ≈ 0.0741
- A driver comes to pick up members of your family for a family reunion. The van holds 7 people, not including the driver. Assuming that none of the babies will be riding in the van, how many different ways can 7 people be chosen to ride in the van?
Since the babies are not included, we have 6 people to choose from (A, B, C, E, G, H).
The number of ways to choose 7 people from 6 is represented by 6C7 or 6! / (7! * (6-7)!) = 0, as we don't have enough people to satisfy the condition.
Please note that the numbers and calculations provided here are based on the data given in the question.