💣 Q :150 Prep 1 Question Bank T1

a) For a set of values: If \(\sum f = 10\) and \(\sum (f \cdot X) = 40\), then what is the value of \(\overline{X}\)?

(a) 4

(b) 30

(c) 50

(d) 400

\[ \overline{X} = \frac{\sum (f \cdot X)}{\sum f} = \frac{40}{10} = \boxed{4} \]

MR/Nasef.N

b) 55, 75, 55, 42, and 47 represent the numbers of children who took the infantile paralysis vaccine over five days. If the number of children who took the vaccine on the sixth day is 95, then which of the following statements is true?

(a) The median decreases

(b) The mode increases

(c) The average decreases

(d) The average increases

Original data: 42, 47, 55, 55, 75

With 6th day (95): 42, 47, 55, 55, 75, 95

Original average: \(\frac{42+47+55+55+75}{5} = 54.8\)

New average: \(\frac{42+47+55+55+75+95}{6} = 61.5\)

The average \(\boxed{\text{increases}}\) from 54.8 to 61.5