This median practice worksheet challenges students to calculate the median in real-world scenarios involving weekly savings, family ages, and census years.

Let's solve each question step by step and explain the reasoning.

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Question 1:

Michael’s grandparents gave him a piggy bank with $10 for his birthday. Michael added $2 each week to the piggy bank and recorded how much money he had in it at the end of each week. If he did this for 9 weeks after his birthday, what is the median of the amounts he recorded during these weeks?

#### Step-by-step:
- Initial amount: $10
- Each week, he adds $2.
- So, the amount at the end of each week forms an arithmetic sequence:
- Week 1: $10 + $2 = $12
- Week 2: $12 + $2 = $14
- Week 3: $16
- ...
- Week 9: $10 + (9 × $2) = $10 + $18 = $28

So, the amounts recorded over the 9 weeks are:

> $12, $14, $16, $18, $20, $22, $24, $26, $28

This is an ordered list (already in ascending order).

To find the median, we look for the middle value in an ordered list.

Since there are 9 values (odd number), the median is the 5th value.

Counting:
1. $12
2. $14
3. $16
4. $18
5. $20 ← Median
6. $22
7. $24
8. $26
9. $28

✔ Median = $20

Answer: b. $20

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Question 2:

Jeremy has 2 brothers and 3 sisters. His brothers are 1 year younger and 4 years younger than him. His sisters are 1 year, 4 years, and 6 years older than him. Jeremy is 9 years old. What is the median age of Jeremy and his brothers and sisters?

#### Step-by-step:
We need to find the ages of all siblings and then compute the median.

Jeremy’s age = 9

Brothers:
- 1 year younger → 9 - 1 = 8
- 4 years younger → 9 - 4 = 5

Sisters:
- 1 year older → 9 + 1 = 10
- 4 years older → 9 + 4 = 13
- 6 years older → 9 + 6 = 15

Now list all the ages:
- Brothers: 8, 5
- Sisters: 10, 13, 15
- Jeremy: 9

All ages: 5, 8, 9, 10, 13, 15

Wait — that's 6 people total: Jeremy + 2 brothers + 3 sisters = 6

List them in order:
> 5, 8, 9, 10, 13, 15

Even number of values → median is the average of the two middle numbers.

Middle positions: 3rd and 4th values → 9 and 10

Median = (9 + 10) / 2 = 9.5

✔ Answer: b. 9.5

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Question 3:

Starting in 2000, a city-wide census was taken every 2 years until 2010. What was the median year of the years in which the censuses were taken during that time?

#### Step-by-step:
Census years: every 2 years from 2000 to 2010 inclusive.

List the years:
- 2000
- 2002
- 2004
- 2006
- 2008
- 2010

That’s 6 years.

Ordered list: 2000, 2002, 2004, 2006, 2008, 2010

Even number of values → median = average of 3rd and 4th values

3rd: 2004
4th: 2006

Median = (2004 + 2006) / 2 = 2005

✔ Answer: b. 2005

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✔ Final Answers:

1. b. $20
2. b. 9.5
3. b. 2005

Let me know if you'd like this formatted as a completed worksheet!