first and third quartile for 1.6 1.9 7.5 7.8 18.2 22.3 24.2 24.6 25.9 29.4

The position of the first quartile is 25% of the total data points. Since we have 10 data points, the position of Q1 is at the 2.5th data point (rounded up to the nearest whole number).

The value at the 2.5th position is the average of the second and third data points:

Q1 = (1.9 + 7.5) / 2 = 4.7

Third Quartile (Q3): Again, arrange the data in ascending order:

1.6, 1.9, 7.5, 7.8, 18.2, 22.3, 24.2, 24.6, 25.9, 29.4

The position of the third quartile is 75% of the total data points. So, Q3 is at the 7.5th data point (rounded up to the nearest whole number).

The value at the 7.5th position is the average of the seventh and eighth data points:

Q3 = (24.2 + 24.6) / 2 = 24.4

Therefore:

First Quartile (Q1) ≈ 4.7

Third Quartile (Q3) ≈ 24.4

msm555 msm555 · Answer 2 · 2024-01-15T06:54:14+01:00

Answer:

first quartile [tex](Q_1) = 7.5 [/tex]

third quartile [tex](Q_3) = 24.6 [/tex]

Step-by-step explanation:

Arrange the data in ascending order:

[tex]1.6, 1.9, 7.5, 7.8, 18.2, 22.3, 24.2, 24.6, 25.9, 29.4[/tex]

Calculate the quartile position [tex](Q_p)[/tex]:

[tex]Q_p = \dfrac{(n + 1)}{4}[/tex]

[tex]Q_p = \dfrac{(10 + 1)}{4 }\\\\ \dfrac{11}{4}\\\\= 2.75[/tex]

Determine the first quartile [tex](Q_1)[/tex]:

[tex]Q_1[/tex] = the value at the 3rd position (2.75 rounds down to 3:

[tex]Q_1[/tex] = 7.5

Determine the third quartile [tex](Q_3)[/tex]:

[tex]Q_3[/tex] = the value at the 8th position [tex](2.75 \times 3 = 8.25[/tex] rounds down to 8)

[tex]Q_3[/tex] = 24.6

Therefore, the first quartile [tex](Q_1)[/tex] is 7.5, and the third quartile [tex](Q_3)[/tex] is 24.6.