Question

write the five - number summary for each set of data.

1. 42, 58, 67, 55, 40, 69, 66, 51, 46, 48, 68

minimum:
q1:
q2:
q3:
maximum:

1. 14, 11, 8, 1, 23, 20, 17, 5, 19, 10, 12, 22

minimum:
q1:
q2:
q3:
maximum:

1. 107, 92, 111, 119, 99, 100, 89, 94, 125, 93

minimum:
q1:
q2:
q3:
maximum:

1. 72, 63, 51, 75, 79, 63, 70, 61, 78

minimum:
q1:
q2:
q3:
maximum:

1. 21, 4, 18, 9, 25, 16, 27, 30, 33, 15, 31

minimum:
q1:
q2:
q3:
maximum:

1. 134, 47, 122, 113, 49, 56, 102, 93, 62

minimum:
q1:
q2:
q3:
maximum:

Explanation:

Step1: Sort the data

For the first set 42, 58, 67, 55, 40, 69, 66, 51, 46, 48, 68: sorted it is 40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69.

Step2: Find the minimum

The minimum is the first - value in the sorted list. For the sorted first - set, minimum = 40.

Step3: Find the first quartile ($Q_1$)

The position of $Q_1$ is $\frac{n + 1}{4}$ for $n = 11$. $\frac{11+1}{4}=3$. So $Q_1$ is the 3rd value in the sorted list, $Q_1 = 46$.

Step4: Find the median ($Q_2$)

The position of the median for $n = 11$ is $\frac{n + 1}{2}=6$. So $Q_2=55$.

Step5: Find the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9$. So $Q_3 = 66$.

Step6: Find the maximum

The maximum is the last - value in the sorted list. For the first - set, maximum = 69.

Repeating these steps for the other sets:

1. For 42, 58, 67, 55, 40, 69, 66, 51, 46, 48, 68:

• Minimum: 40
• $Q_1$: 46
• $Q_2$: 55
• $Q_3$: 66
• Maximum: 69

1. For 14, 11, 8, 1, 23, 20, 17, 5, 19, 10, 12, 22:

• Sort: 1, 5, 8, 10, 11, 12, 14, 17, 19, 20, 22, 23
• Minimum: 1
• $Q_1$: 8
• $Q_2$: 12.5 ($\frac{12 + 14}{2}$)
• $Q_3$: 19
• Maximum: 23

1. For 107, 92, 111, 119, 99, 100, 89, 94, 125, 93:

• Sort: 89, 92, 93, 94, 99, 100, 107, 111, 119, 125
• Minimum: 89
• $Q_1$: 93
• $Q_2$: 99.5 ($\frac{99+100}{2}$)
• $Q_3$: 111
• Maximum: 125

1. For 72, 63, 51, 75, 79, 63, 70, 61, 78:

• Sort: 51, 61, 63, 63, 70, 72, 75, 78, 79
• Minimum: 51
• $Q_1$: 63
• $Q_2$: 70
• $Q_3$: 75
• Maximum: 79

1. For 21, 4, 18, 9, 25, 16, 27, 30, 33, 15, 31:

• Sort: 4, 9, 15, 16, 18, 21, 25, 27, 30, 31, 33
• Minimum: 4
• $Q_1$: 15
• $Q_2$: 21
• $Q_3$: 27
• Maximum: 33

1. For 134, 47, 122, 113, 49, 56, 102, 93, 62:

• Sort: 47, 49, 56, 62, 93, 102, 113, 122, 134
• Minimum: 47
• $Q_1$: 56
• $Q_2$: 93
• $Q_3$: 113
• Maximum: 134

Answer:

1. Minimum: 40, $Q_1$: 46, $Q_2$: 55, $Q_3$: 66, Maximum: 69
2. Minimum: 1, $Q_1$: 8, $Q_2$: 12.5, $Q_3$: 19, Maximum: 23
3. Minimum: 89, $Q_1$: 93, $Q_2$: 99.5, $Q_3$: 111, Maximum: 125
4. Minimum: 51, $Q_1$: 63, $Q_2$: 70, $Q_3$: 75, Maximum: 79
5. Minimum: 4, $Q_1$: 15, $Q_2$: 21, $Q_3$: 27, Maximum: 33
6. Minimum: 47, $Q_1$: 56, $Q_2$: 93, $Q_3$: 113, Maximum: 134