Question

Answer question 55.51 These 15 ages of students at an after-schoolevent are in order from least to greatest.6, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 18What is the Minimum number of this data?A 1B 3C7D 651

Answer 1

Given:

Given the data set

6, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 18

Required: Interquartile range

Explanation:

Sample size is n = 15.

First, arrange the data set in ascending order.

6, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 18

Compute the quartiles Q1 and Q3.

$\begin{gathered} Q_1=(\frac{n+1}{4})^{t\text{h }}\text{ term} \\ =(\frac{15+1}{4})^{th}\text{ term} \\ =4^{th}\text{ term} \\ =7 \end{gathered}$$\begin{gathered} Q_3=(\frac{3(n+1)}{4})^{th}\text{ term} \\ =(\frac{3(15+1)}{4})^{th}\text{ term} \\ =12^{th}\text{ term} \\ =13 \end{gathered}$

The interquartile range is

$\begin{gathered} IQR=Q_3-Q_1 \\ =13-7 \\ =6 \end{gathered}$

Final Answer: The interquartile range of the given data set is 6.