Question

or questions 1-4. Use the data for The ages of the children at a birthday party are 7, 46, 29, 38 shown below. ile of the data? 7, 5, 10, 9, 15, 12, 6, 9, 7, 10 5. What is the first quartile of the data? A. 5 B. 6 C. 7 7 of the data? D. 9 6. What is the third quartile of the data? A. 9 B 10

Answer 1

#5: Option C

#6: Option B

We are given data and we are required to calculate the 1st quartile and the 3rd quartile.

The formula for calculating this is:

`\begin{gathered} Q_i=(\mleft(i\mleft(n+1\mright)\mright))/(4)^(th) \\ \text{where i= 1, 2, 3, 4} \\ n=\text{ number of values in the data} \end{gathered}`

But before we can use this formula, we must rearrange the data in ascending order:

5, 6, 7, 7, 9, 9, 10 , 10, 12, 15

There are 10 numbers, therefore, n = 10

Thus we can now calculate the Quartiles

`\begin{gathered} Q_1=(1*(10+1))/(4)^(th) \\ Q_1=(11)/(4)=2.75\approx3^(rd) \end{gathered}`

Therefore the first Quartile is in the 3rd position of the arranged data set.

Thus The first Quartile Q1 = 7.

For the 3rd Quartile:

`\begin{gathered} Q_3=((3*(10+1)))/(4)^(th) \\ Q_3=3*(11)/(4) \\ Q_3=8.25\approx8^(th) \end{gathered}`

Therefore the 3rd Quartile is in the 8th position.

Thus, the Third Quartile Q3 = 10

Final Answer:

#5: Option C

#6: Option B