Question

the date of me will give the speed of measured by radar of a random sample of 12 Vehicles traveling on I-95 calculate the first second and third quartile of the data also determined that the interquartile range

Answer 1

We must calculate the first, second and third quartiles of a set of data.

1) First, we must order the data from the lower numbers to the higher:

$61,65,67,68,68,70,77,80,87,88,103,105$

Now, we separate the data into two halves (the red line), and each half in another two halves (the blue lines):

2) From the picture above we see that:

- For the red line, we have the values 70 and 77 on each side, the mid-value between them is:

$q_{50}_{}=\frac{70+77}{2}=73.5$

This value is the 50th percentile quartile.

- For the first line in blue, we have the values 67 and 68 on each side, the mid-value between them is:

$q_{25}=\frac{67+68}{2}=67.5$

This value is the 25th percentile quartile.

- For the second line in blue, we have the values 87 and 88, the mid-value between them is:

$q_{75}=\frac{87+88}{2}=87.5$

3) In summary, the first (Q1), second (Q2), third (Q3) quartiles and interquartile (IQR) of the data are:

$\begin{gathered} Q_1=q_{25}=67.5_{} \\ Q_2=q_{50}=73.5 \\ Q_3=q_{75}=87.5 \\ IQR=Q_3-Q_1=87.5-67.5=20 \end{gathered}$