Question

On a group trip to a certain city, 20 people whowere 25 years old, 20 people who were 30 yearsold, and 20 people who were 35 years oldpurchased tickets for a bus tour of the city. Noone else purchased tickets for the bus tour. A30-year old who had purchased a ticket becameill and did not go on the bus tour, and everyoneelse who purchased a ticket went on the bus tour.Which of the following statements is true? A) The standard deviation of the ages of thepeople who went on the bus tour is greaterthan the standard deviation of the ages ofthe people who purchased tickets.(B) The standard deviation of the ages of thepeople who went on the bus tour is less thanthe standard deviation of the ages of thepeople who purchased tickets.(C) The standard deviation of the ages of thepeople who went on the bus tour is equal tothe standard deviation of the ages of thepeople who purchased tickets.(D) There is not enough information todetermine which standard deviation isgreater.

Answer 1

SOLUTION

Write out the information given.

$\begin{gathered} 25\text{years}=20\text{people} \\ 30\text{years}=20\text{people } \\ 35\text{year}=20\text{people} \end{gathered}$

From the information given, we have the table below

Then the standard deviation becomes

$sd=4.12$

Hence

The standard deviation for ages of the people who puchase the ticket is 4.12

When the 39 years old who had purchased a ticket did not go for the trip, the table becomes

Then the standard deviation becomes

$Sd=4.15$

The standard deviation of the people who went on the bus tour is 4.15

Hence

$4.15\text{ >4.12}$

Hence

The standard deviation of the ages of the people who went on the bus tour is greater than the standard deviation of the ages of the people who purchased tickets.

Answer= Option A