Answer:
(a) There are outliers
(b) [tex]x <-14[/tex] and [tex]x >62[/tex]
Step-by-step explanation:
Given
[tex]\sigma = 14.92[/tex]
[tex]\bar x = 22.0[/tex]
[tex]q_0 = -24[/tex]
[tex]q_1 = 14.5[/tex]
[tex]q_2 = 24.5[/tex]
[tex]q_3 = 33.5[/tex]
[tex]q_4 = 64[/tex]
Solving (a): Check for outliers
This is calculated using:
[tex]Lower = Q_1 - (1.5 * IQR)[/tex] --- lower bound of outlier
[tex]Upper = Q_3 +(1.5 * IQR)[/tex] --- upper bound of outlier
Where
[tex]IQR = Q_3 - Q_1[/tex]
So, we have:
[tex]IQR = 33.5 - 14.5[/tex]
[tex]IQR = 19[/tex]
The lower bound of outlier becomes
[tex]Lower = Q_1 - (1.5 * IQR)[/tex]
[tex]Lower = 14.5 - (1.5 * 19)[/tex]
[tex]Lower = 14.5 - 28.5[/tex]
[tex]Lower = -14[/tex]
The upper bound of outlier becomes
[tex]Upper = Q_3 +(1.5 * IQR)[/tex]
[tex]Upper = 33.5 + 1.5 * 19[/tex]
[tex]Upper = 33.5 + 28.5[/tex]
[tex]Upper = 62[/tex]
So, we have:
[tex]-14 \le x \le 62[/tex] --- the range without outlier
Given that:
[tex]q_0 = -24[/tex] --- This represents the lowest data
[tex]q_4 = 64[/tex] --- This represents the highest data
-24 and 64 are out of range of [tex]-14 \le x \le 62[/tex].
Hence, there are outliers
Solving (b): The outliers
The outliers are data less than the lower bound (i.e. less than -14) or greater than the upper bound (i.e. 62)
So, the outliers are:
[tex]x <-14[/tex] and [tex]x >62[/tex]
