Math worksheet on median, mode, range, and mean with sports-themed examples.

Here are the step-by-step solutions for the problems on the worksheet.

Part 1: Athletics Team Times (Running)

Data:
The times given are: 55, 60, 47, 56, 55, 49, 53, 55, 56.

Step 1: Put the times in order (Question 1)
To find the median and range easily, we first list the numbers from smallest (quickest) to largest (slowest).
* Smallest: 47
* Next: 49
* Next: 53
* Next: 55, 55, 55 (There are three of these)
* Next: 56, 56 (There are two of these)
* Largest: 60

Ordered List: 47, 49, 53, 55, 55, 55, 56, 56, 60

Step 2: Find the Median (Question 2)
The median is the middle number. Since there are 9 numbers, the middle one is the 5th number.
Counting into our ordered list: 47, 49, 53, 55, 55, 55, 56, 56, 60.
The middle number is 55.

Step 3: Find the Mode (Question 3)
The mode is the number that appears most often.
* 55 appears 3 times.
* 56 appears 2 times.
* All others appear once.
The mode is 55.

Step 4: Find the Range (Question 4)
The range is the difference between the biggest and smallest numbers.
* Biggest: 60
* Smallest: 47
* Calculation: $60 - 47 = 13$
The range is 13.

Step 5: Find the Mean (Question 5)
The mean is the average. We add all the numbers together and divide by how many numbers there are (9).
* Sum: $47 + 49 + 53 + 55 + 55 + 55 + 56 + 56 + 60 = 486$
* Divide by 9: $486 \div 9 = 54$
The mean is 54.

***

Part 2: Cricket Scores

Data:
The scores given are: 56, 42, 12, 84, 111, 42, 76, 9, 99.

Step 6: Find the Median Score (Question 6)
First, put the scores in order from smallest to largest:
9, 12, 42, 42, 56, 76, 84, 99, 111.
There are 9 scores. The middle score is the 5th one.
Counting in: 9, 12, 42, 42, 56, 76, 84, 99, 111.
The median is 56.

Step 7: Find the Mode (Question 7)
Look for the number that repeats.
* 42 appears twice.
* All other numbers appear only once.
The mode is 42.

Step 8: Find the Range (Question 8)
Subtract the smallest score from the largest score.
* Largest: 111
* Smallest: 9
* Calculation: $111 - 9 = 102$
The range is 102.

Step 9: Total Score (Question 9)
Add all the scores together.
$56 + 42 + 12 + 84 + 111 + 42 + 76 + 9 + 99 = 531$
He scored 531 altogether.

Step 10: Find the Mean (Question 10)
Divide the total score by the number of games (9).
* Calculation: $531 \div 9 = 59$
The mean is 59.

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Final Answer:

1. 47 min, 49 min, 53 min, 55 min, 55 min, 55 min, 56 min, 56 min, 60 min
2. 55
3. 55
4. 13
5. 54
6. 56
7. 42
8. 102
9. 531
10. 59