Question

1. a runners 5k split times (min) are: 21.6, 24.3, 22.8, 23.1, 25.2. what is the mean time?

a. 23.0
b. 23.4
c. 23.6
d. 23.8

1. post-exercise heart rates (bpm) are: 148, 152, 145, 160, 150. what is the median?

a. 148
b. 150
c. 152
d. 155

1. sprint times (s) for 6 athletes: 11.2, 10.8, 11.5, 10.9, 11.0, 11.1. what is the median?

a. 11.0
b. 11.05
c. 11.1
d. 11.2

1. grip strength scores (kg) are: 42, 45, 45, 47, 50, 45, 52. what is the mode?

a. 42
b. 45
c. 47
d. 50

1. vertical jump heights (cm) are: 48, 55, 51, 60, 52. what is the range?

a. 8
b. 10
c. 12
d. 15

1. two training groups have the same mean vo₂max, but group as values are much more spread out than group bs. which statement is true?

a. group a has a smaller standard deviation
b. group a has a larger standard deviation
c. both groups must have the same standard deviation
d. standard deviation cant be compared if means are equal

1. a set of resting heart rates (bpm) is: 58, 60, 61, 62, 120. compared to the dataset without the 120, which statement is true?

a. mean increases a lot; median stays about the same
b. mean stays the same; median increases a lot
c. mean decreases; median decreases
d. mean and median both stay the same

Explanation:

Step1: Calculate mean (Q1)

Sum values: $21.6 + 24.3 + 22.8 + 23.1 + 25.2 = 117$
Mean: $\frac{117}{5} = 23.4$

Step2: Find median (Q2)

Sort data: $145, 148, 150, 152, 160$
Median = 3rd value: $150$

Step3: Find median (Q3)

Sort data: $10.8, 10.9, 11.0, 11.1, 11.2, 11.5$
Average 3rd/4th values: $\frac{11.0 + 11.1}{2} = 11.05$

Step4: Identify mode (Q4)

Count frequencies: $45$ appears 3 times (most frequent)

Step5: Calculate range (Q5)

Range = Max - Min: $60 - 48 = 12$

Step6: Interpret standard deviation (Q6)

Larger spread = larger standard deviation

Step7: Analyze outlier effect (Q7)

Outlier 120 increases mean; median of original data ($58,60,61,62,120$) is 61, median without 120 ($58,60,61,62$) is $\frac{60+61}{2}=60.5$ (stays similar)

Answer:

1. b. 23.4
2. b. 150
3. b. 11.05
4. b. 45
5. c. 12
6. b. Group A has a larger standard deviation
7. a. Mean increases a lot; median stays about the same