Question

find the quartiles for each set of numbers.

1. 32, 13, 46, 28, 51, 62, 19, 38, 73, 47

first quartile :
second quartile :
third quartile :

1. 98, 36, 82, 61, 73, 48, 58, 39

first quartile :____ second quartile :__ third quartile :____

1. 64,7,34,53,28,41,13,72,10

first quartile :____ second quartile :__ third quartile :____

1. 13,63,29,19,71,56

first quartile :____ second quartile :__ third quartile :____

1. the average hibernation periods (in weeks) of alpine marmots, common poorwills, american black bears, bats, dwarf lemurs, box turtles and bumblebees were recorded by a zoologist.

28, 15, 15, 46, 27, 21, 24
find the first, second and third quartiles.
first quartile :____ second quartile :__ third quartile :____

Explanation:

Step1: Arrange the data in increasing order

For problem 2: \(36,39,48,58,61,73,82,98\)
For problem 3: \(7,10,13,28,34,41,53,64,72\)
For problem 4: \(13,19,29,56,63,71\)
For problem 5: \(15,15,21,24,27,28,46\)

Step2: Calculate the second quartile (median)

• Problem 2:

Since \(n = 8\) (even), \(Q_{2}=\frac{58 + 61}{2}=\frac{119}{2}=59.5\)

• Problem 3:

Since \(n=9\) (odd), \(Q_{2}=34\)

• Problem 4:

Since \(n = 6\) (even), \(Q_{2}=\frac{29+56}{2}=\frac{85}{2} = 42.5\)

• Problem 5:

Since \(n=7\) (odd), \(Q_{2}=24\)

Step3: Calculate the first quartile (\(Q_{1}\))

• Problem 2:

The lower half is \(36,39,48,58\). Since \(n = 4\) (even), \(Q_{1}=\frac{39+48}{2}=\frac{87}{2}=43.5\)

• Problem 3:

The lower half is \(7,10,13,28\). Since \(n = 4\) (even), \(Q_{1}=\frac{10 + 13}{2}=\frac{23}{2}=11.5\)

• Problem 4:

The lower half is \(13,19\). Since \(n = 2\) (even), \(Q_{1}=\frac{13+19}{2}=\frac{32}{2}=16\)

• Problem 5:

The lower half is \(15,15,21\). Since \(n = 3\) (odd), \(Q_{1}=15\)

Step4: Calculate the third quartile (\(Q_{3}\))

• Problem 2:

The upper half is \(61,73,82,98\). Since \(n = 4\) (even), \(Q_{3}=\frac{73+82}{2}=\frac{155}{2}=77.5\)

• Problem 3:

The upper half is \(41,53,64,72\). Since \(n = 4\) (even), \(Q_{3}=\frac{53+64}{2}=\frac{117}{2}=58.5\)

• Problem 4:

The upper half is \(56,63\). Since \(n = 2\) (even), \(Q_{3}=\frac{56+63}{2}=\frac{119}{2}=59.5\)

• Problem 5:

The upper half is \(27,28,46\). Since \(n = 3\) (odd), \(Q_{3}=28\)

Answer:

1. First quartile: \(23.5\), Second quartile: \(42\), Third quartile: \(54.5\) (assuming the first - problem's correct calculation as per the method above, the user's hand - written answer in the first problem seems wrong. But following the steps: for \(13,19,28,32,38,46,47,51,62,73\) (after sorting), \(n = 10\), \(Q_{2}=\frac{38 + 46}{2}=42\), lower half \(13,19,28,32,38\), \(Q_{1}=\frac{19+28}{2}=23.5\), upper half \(46,47,51,62,73\), \(Q_{3}=\frac{51+62}{2}=56.5\))
2. First quartile: \(43.5\), Second quartile: \(59.5\), Third quartile: \(77.5\)
3. First quartile: \(11.5\), Second quartile: \(34\), Third quartile: \(58.5\)
4. First quartile: \(16\), Second quartile: \(42.5\), Third quartile: \(59.5\)
5. First quartile: \(15\), Second quartile: \(24\), Third quartile: \(28\)