Description
Chamberlain University
MATH 225N- Statistical Reasoning for the health Sciences
Week 3: Measures of Central Tendency
Question
Find the median of the following set of miles per gallon for randomly selected sports cars.
36,22,24,30,44,13,21,34,18
Answer Explanation
Correct answers:
median=24 miles per gallon
It helps to put the numbers in order.
13,18,21,22,24,30,34,36,44
Now, because the list has length 9, which is odd, we know the median number will be the middle number. In other words, we can count to item 5 in the list, which is 24. So the median number of miles per gallon for the randomly selected sports cars is 24.
Question
What is the mean of the following list of numbers?
7,11,6,14,12
Answer Explanation
Correct answers:
- mean=10
Remember that the mean is the sum of the numbers divided by the number of numbers. There are 5 numbers in the list. So we find that the mean is
(7+11+6+14+12)/5
=50/5
=10
Question
The football coach wants to know the average number of points scored by the team in their last few games. The scores are listed below.
38,40,18,40,14
Find the mean points scored.
Answer Explanation
Correct answers:
- mean=30 points
Remember that the mean is the sum of the numbers divided by the number of numbers. There are 5 numbers in the list. So we find that the mean points scored is
(38+40+18+40+14)/ 5
=150/ 5
=30
Question
Find the median of the following tips (in dollars) earned in the last hour by waiters in an Italian restaurant.
4,9,6,27,17,10,14,26
Correct answers:
- median=12 dollars
It helps to put the numbers in order.
4,6,9,10,14,17,26,27
Now, because the list has length 8, which is even, we know the median number will be the average of the middle two numbers, 10 and 14. So the median amount of tips (in dollars) earned in the last hour by waiters in an Italian restaurant is 12
Question
Find the mode of the following amounts of exercise (in hours) randomly selected runners completed during a weekend.
2,14,14,4,2,4,1,14,4,4,8
Answer Explanation
Correct answers:
- mode=4 hours
If we count the number of times each value appears in the list, we get the following frequency table:
| Value | Frequency |
| 1 | 1 |
| 2 | 2 |
| 4 | 4 |
| 8 | 1 |
| 14 | 3 |
Note that 4 occurs 4 times, which is the greatest frequency, so 4 is the mode of the amount of exercise (in hours) randomly selected runners completed during a weekend.
Question
Find the mode of the following number of countries randomly selected travelers visited in the past two years.
13,13,15,7,8,4,4,7,13
Answer Explanation
Correct answers:
- $\text{mode=}13\text{ countries}$mode=13 countries
If we count the number of times each value appears in the list, we get the following frequency table:
| Value | Frequency |
| 4 | 2 |
| 7 | 2 |
| 8 | 1 |
| 13 | 3 |
| 15 | 1 |
Note that 13 occurs 3 times, which is the greatest frequency, so 13 is the mode of the number of countries randomly selected travelers visited in the past two years.
Question
Find the mode of the following number of times each machine in a car factory needed to be fixed within the last year.
2,5,6,12,14,12,6,2,5,3,14,5
Answer Explanation
Correct answers:
- $\text{mode=}5\text{ repairs}$mode=5 repairs
If we count the number of times each value appears in the list, we get the following frequency table:
| Value | Frequency |
| 2 | 2 |
| 3 | 1 |
| 5 | 3 |
| 6 | 2 |
| 12 | 2 |
| 14 | 2 |
Note that 5 occurs 3 times, which is the greatest frequency, so 5 is the mode of the number of times a machine in a car factory needed to be fixed within the last year.
Question
Find the mode of the following number of states randomly selected travelers at a service plaza visited in the past three years.
18,13,8,8,13,10,13,10,9,18
Answer Explanation
Correct answers:
- $\text{mode=}13\text{ states}$mode=13 states
If we count the number of times each value appears in the list, we get the following frequency table:
| Value | Frequency |
| 8 | 2 |
| 9 | 1 |
| 10 | 2 |
| 13 | 3 |
| 18 | 2 |
Note that 13 occurs 3 times, which is the greatest frequency, so 13 is the mode of the number of states randomly selected travelers at a service plaza visited in the past three years.
Question
An art collector bought 20 paintings at an art fair and wants to know the average price of the paintings she purchased at the fair. She adds the prices of all the paintings and divides this number by 20 to find an average price of $350. Is this price a sample mean or a population mean, and which symbol would be used to denote it?
- Sample Mean μ
- Population Mean μ
- Sample Mean x¯¯¯
- Population Mean x¯¯¯
Answer Explanation
Correct answer:
Population Mean μ
The Population Mean is an average calculated on the entire group under study. In this example, the art collector was interested in studying the price of the 20 paintings she had just purchased. Since the mean was calculated based on the entire group under study, this indicates that the average price of $350 represents the population mean, which is denoted by the symbol μ.
Question
A track and field coach wants to study the average 100-meter dash time of his team. A random selection of half the team has a mean time of 13 seconds. Is this mean considered a sample mean or a population mean, and which symbol would be used to denote it?
- Population Mean μ
- Sample Mean μ
- Sample Mean x¯¯¯
- Population Mean x¯¯¯
Answer Explanation
Correct answer:
Sample Mean x¯¯¯
The sample mean is an average calculated on a sample taken from the entire group of interest. In this example, a sample of half the team was taken from the larger group consisting of the entire team. Since the mean was calculated on this subset, 13 seconds represents a sample mean, which is denoted by x¯¯¯.
Question
Given the following list of data, find the median.
22,33,17,8,17,29,18,13,26,28
- 13
- 20
- 18
- 29
- 33
- 17
Answer Explanation
Correct answer:
20
It helps to put the numbers in order.
8,13,17,17,18,22,26,28,29,33
Now, because the list has length 10, which is even, we know the median number will be the average of the middle two numbers, 18 and 22. So the median is 20.
Question
Find the median of the numbers in the following list.
36,26,22,39,25,37,32,24,46,22,28
Give your answer as a number only. For example, if you found the median was 30, you would enter 30.
Answer Explanation
Correct answers:
- 28
It helps to put the numbers in order.
22,22,24,25,26,28,32,36,37,39,46
Now, because the list has length 11, which is odd, we know the median number will be the middle number. In other words, we can count to item 6 in the list, which is 28. So the median is 28.
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