Question

A surfer recorded the maximum wave height each day at the beach for 10 days. The results are shown in this dot plot.

Answer 1

Answer:

The correct option is 3. The 10 foot wave is an outlier.

Step-by-step explanation:

The height of waves for 10 days are shown in the given figure.

From the figure it is noticed that the height of wave length is 2 for 5 days, 3 for 4 days and 10 for 1 day.

If arrange the height of wave in ascending order we get

$2,2,2,2,2,3,3,3,3,10$

Total number of observation is 10.

$Q_1=\frac{n}{4}\text{th term}$

$Q_1=\frac{10}{4}\text{th term}=2.5\text{th term}$

It means Q₁ is the average of second and third term.

$Q_1=\frac{2+2}{2}=2$

$Q_3=\frac{3n}{4}\text{th term}$

$Q_3=\frac{3(10)}{4}\text{th term}=7.5\text{th term}$

It means Q₃ is the average of seventh and eight th term.

$Q_3=\frac{3+3}{2}=3$

Interquartile range is the difference between Q₃ and Q₁.

$I.Q.=Q_3-Q_1=3-2=1$

$Q_1-1.5(I.Q.)=2-1.5=0.5$

$Q_3+1.5(I.Q.)=3+1.5=4.5$

Therefore the data which lies outsides $[0.5,4.5]$ are outliers of the data.

Thus, the correct option is 3. The 10 foot wave is an outlier.