Question

calculate the median for each of the sets of numbers:

1. 34, 43, 45, 1, 30, 4 median =
2. 7, 32, 1, 28, 43, 37 median =
3. 35, 33, 15, 32, 2, 28, 42 median =
4. 29, 3, 42, 17, 17, 48, 7 median =
5. 45, 29, 17, 12, 13, 28 median =
6. 14, 41, 6, 31, 6, 16 median =
7. 35, 4, 16, 36, 46, 42, 17 median =
8. 24, 20, 42, 40, 33, 8 median =
9. 45, 47, 2, 44, 42, 27 median =
10. 28, 4, 23, 9, 28, 16, 39 median =

Explanation:

1. For the set \(34,43,45,1,30,4\)

Step1: Sort the numbers

Sort the numbers from smallest to largest: \(1,4,30,34,43,45\)

Step2: Calculate the median (even - numbered set)

Since there are \(n = 6\) numbers, the median is the average of the \(\frac{n}{2}=3^{rd}\) and \((\frac{n}{2}+ 1)=4^{th}\) numbers. \(\text{Median}=\frac{30 + 34}{2}=\frac{64}{2}=32\)

2. For the set \(7,32,1,28,43,37\)

Step1: Sort the numbers

Sort the numbers: \(1,7,28,32,37,43\)

Step2: Calculate the median (even - numbered set)

With \(n = 6\) numbers, \(\text{Median}=\frac{28+32}{2}=\frac{60}{2} = 30\)

3. For the set \(35,33,15,32,2,28,42\)

Step1: Sort the numbers

Sort the numbers: \(2,15,28,32,33,35,42\)

Step2: Calculate the median (odd - numbered set)

Since \(n = 7\), the median is the \(\frac{n + 1}{2}=4^{th}\) number. \(\text{Median}=32\)

4. For the set \(29,3,42,17,17,48,7\)

Step1: Sort the numbers

Sort the numbers: \(3,7,17,17,29,42,48\)

Step2: Calculate the median (odd - numbered set)

With \(n=7\), the median is the \(\frac{n + 1}{2}=4^{th}\) number. \(\text{Median}=17\)

5. For the set \(45,29,17,12,13,28\)

Step1: Sort the numbers

Sort the numbers: \(12,13,17,28,29,45\)

Step2: Calculate the median (even - numbered set)

Since \(n = 6\), \(\text{Median}=\frac{17+28}{2}=\frac{45}{2}=22.5\)

6. For the set \(14,41,6,31,6,16\)

Step1: Sort the numbers

Sort the numbers: \(6,6,14,16,31,41\)

Step2: Calculate the median (even - numbered set)

With \(n = 6\), \(\text{Median}=\frac{14 + 16}{2}=\frac{30}{2}=15\)

7. For the set \(35,4,16,36,46,42,17\)

Step1: Sort the numbers

Sort the numbers: \(4,16,17,35,36,42,46\)

Step2: Calculate the median (odd - numbered set)

Since \(n = 7\), the median is the \(\frac{n+1}{2}=4^{th}\) number. \(\text{Median}=35\)

8. For the set \(24,20,42,40,33,8\)

Step1: Sort the numbers

Sort the numbers: \(8,20,24,33,40,42\)

Step2: Calculate the median (even - numbered set)

With \(n = 6\), \(\text{Median}=\frac{24+33}{2}=\frac{57}{2}=28.5\)

9. For the set \(45,47,2,44,42,27\)

Step1: Sort the numbers

Sort the numbers: \(2,27,42,44,45,47\)

Step2: Calculate the median (even - numbered set)

Since \(n = 6\), \(\text{Median}=\frac{42+44}{2}=\frac{86}{2}=43\)

10. For the set \(28,4,23,9,28,16,39\)

Step1: Sort the numbers

Sort the numbers: \(4,9,16,23,28,28,39\)

Step2: Calculate the median (odd - numbered set)

With \(n = 7\), the median is the \(\frac{n + 1}{2}=4^{th}\) number. \(\text{Median}=23\)

Answer:

1. \(32\)
2. \(30\)
3. \(32\)
4. \(17\)
5. \(22.5\)
6. \(15\)
7. \(35\)
8. \(28.5\)
9. \(43\)
10. \(23\)