Question

write out the five number summary for each data set.

1. 18, 25, 46, 38, 40, 24, 45, 6, 49, 5

minimum: ____________
$q_1$: ____________
$q_2$: ____________
$q_3$: ____________
maximum: ____________

1. 48, 7, 31, 44, 10, 34, 50, 45, 29, 36, 46, 15

minimum: ____________
$q_1$: ____________
$q_2$: ____________
$q_3$: ____________
maximum: ____________

1. 9, 24, 27, 28, 40, 7, 36, 14, 12, 16, 25

minimum: ____________
$q_1$: ____________
$q_2$: ____________
$q_3$: ____________
maximum: ____________

1. 17, 22, 47, 33, 13, 2, 27, 32, 44, 28, 37, 48

minimum: ____________
$q_1$: ____________
$q_2$: ____________
$q_3$: ____________
maximum: ____________

1. 36, 28, 3, 14, 34, 11, 37, 17, 8, 7, 2

minimum: ____________
$q_1$: ____________
$q_2$: ____________
$q_3$: ____________
maximum: ____________

1. 42, 46, 34, 14, 8, 21, 11, 13, 50, 39, 19, 33, 32

minimum: ____________
$q_1$: ____________
$q_2$: ____________
$q_3$: ____________
maximum: ____________

Explanation:

Step1: Sort each data set

1) Sorted: $5, 6, 18, 24, 25, 38, 40, 45, 46, 49$

2) Sorted: $7, 10, 15, 29, 31, 34, 36, 44, 45, 46, 48, 50$

3) Sorted: $7, 9, 12, 14, 16, 24, 25, 27, 28, 36, 40$

4) Sorted: $2, 13, 17, 22, 27, 28, 32, 33, 37, 44, 47, 48$

5) Sorted: $2, 3, 7, 8, 11, 14, 17, 28, 34, 36, 37$

6) Sorted: $8, 11, 13, 14, 19, 21, 32, 33, 34, 39, 42, 46, 50$

Step2: Find min/max

Minimum = first value; Maximum = last value.

Step3: Calculate $Q_2$ (median)

• Even $n$: $Q_2=\frac{\frac{n}{2}\text{th} + (\frac{n}{2}+1)\text{th}}{2}$
• Odd $n$: $Q_2=(\frac{n+1}{2})\text{th}$ value.

Step4: Calculate $Q_1$ (lower median)

Median of lower half of data.

Step5: Calculate $Q_3$ (upper median)

Median of upper half of data.

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1) Data set: $n=10$

Step1: Min/Max

Minimum = $5$, Maximum = $49$

Step2: Find $Q_2$

$Q_2=\frac{25+38}{2}=31.5$

Step3: Find $Q_1$

Lower half: $5,6,18,24,25$; $Q_1=18$

Step4: Find $Q_3$

Upper half: $38,40,45,46,49$; $Q_3=45$

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2) Data set: $n=12$

Step1: Min/Max

Minimum = $7$, Maximum = $50$

Step2: Find $Q_2$

$Q_2=\frac{31+34}{2}=32.5$

Step3: Find $Q_1$

Lower half: $7,10,15,29,31,34$; $Q_1=\frac{15+29}{2}=22$

Step4: Find $Q_3$

Upper half: $36,44,45,46,48,50$; $Q_3=\frac{45+46}{2}=45.5$

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3) Data set: $n=11$

Step1: Min/Max

Minimum = $7$, Maximum = $40$

Step2: Find $Q_2$

$Q_2=24$ (6th value)

Step3: Find $Q_1$

Lower half: $7,9,12,14,16$; $Q_1=12$

Step4: Find $Q_3$

Upper half: $25,27,28,36,40$; $Q_3=28$

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4) Data set: $n=12$

Step1: Min/Max

Minimum = $2$, Maximum = $48$

Step2: Find $Q_2$

$Q_2=\frac{28+32}{2}=30$

Step3: Find $Q_1$

Lower half: $2,13,17,22,27,28$; $Q_1=\frac{17+22}{2}=19.5$

Step4: Find $Q_3$

Upper half: $32,33,37,44,47,48$; $Q_3=\frac{37+44}{2}=40.5$

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5) Data set: $n=11$

Step1: Min/Max

Minimum = $2$, Maximum = $37$

Step2: Find $Q_2$

$Q_2=14$ (6th value)

Step3: Find $Q_1$

Lower half: $2,3,7,8,11$; $Q_1=7$

Step4: Find $Q_3$

Upper half: $17,28,34,36,37$; $Q_3=34$

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6) Data set: $n=13$

Step1: Min/Max

Minimum = $8$, Maximum = $50$

Step2: Find $Q_2$

$Q_2=32$ (7th value)

Step3: Find $Q_1$

Lower half: $8,11,13,14,19,21$; $Q_1=\frac{13+14}{2}=13.5$

Step4: Find $Q_3$

Upper half: $33,34,39,42,46,50$; $Q_3=\frac{39+42}{2}=40.5$

Answer:

1)
Minimum: $5$
$Q_1$: $18$
$Q_2$: $31.5$
$Q_3$: $45$
Maximum: $49$

2)
Minimum: $7$
$Q_1$: $22$
$Q_2$: $32.5$
$Q_3$: $45.5$
Maximum: $50$

3)
Minimum: $7$
$Q_1$: $12$
$Q_2$: $24$
$Q_3$: $28$
Maximum: $40$

4)
Minimum: $2$
$Q_1$: $19.5$
$Q_2$: $30$
$Q_3$: $40.5$
Maximum: $48$

5)
Minimum: $2$
$Q_1$: $7$
$Q_2$: $14$
$Q_3$: $34$
Maximum: $37$

6)
Minimum: $8$
$Q_1$: $13.5$
$Q_2$: $32$
$Q_3$: $40.5$
Maximum: $50$