Question 38

Consider the data in the following table!

The upper quartile of the data in the table is ....

To calculate the upper quartile from grouped data, use the third quartile formula.

The upper quartile is located at position

f_{K_3} = \frac{3}{4} \cdot n = \frac{3}{4} \cdot 40 = 30

The $30$ th position is in the interval $70$ — $79$

Cumulative frequency before the upper quartile class

f_{ks} = 7 + 11 + 9 = 27

Frequency of the upper quartile class

f_{K_3} = 6

Lower boundary of the upper quartile class

T_b = 70 - 0.5 = 69.5

Class width

c = 79.5 - 69.5 = 10

Using the upper quartile formula for grouped data

K_3 = T_b + \left(\frac{\frac{3}{4}n - f_{ks}}{f_{K_3}}\right) \cdot c

= 69.5 + \left(\frac{30 - 27}{6}\right) \cdot 10

= 69.5 + \frac{3}{6} \cdot 10

= 69.5 + 5

= 74.5

Therefore, the upper quartile of the data in the table is $74.5$

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