Question

(a) find the first quartile. 1.82 (b) find the third quartile. 2.61 (c) find $\bar{x}$. 2.29 (d) find the median. 2.06 (e) find the range. 1.55 (f) find s. 0.45 (g) find the interquartile range. (h) what are the lower and upper limits to find outliers using the iqr rule? ll: ul: (i) find $s^{2}$. question help: message instructor

Explanation:

Step1: Recall IQR formula

The inter - quartile range (IQR) is given by $IQR = Q_3 - Q_1$, where $Q_1$ is the first quartile and $Q_3$ is the third quartile.

Step2: Substitute given values

We are given $Q_1 = 1.82$ and $Q_3=2.61$. So, $IQR=2.61 - 1.82$.

Step3: Calculate IQR

$IQR = 0.79$

Step4: Recall lower and upper limits for outliers

The lower limit (LL) for outliers is $Q_1-1.5\times IQR$ and the upper limit (UL) for outliers is $Q_3 + 1.5\times IQR$.

Step5: Calculate lower limit

$LL=1.82-1.5\times0.79=1.82 - 1.185 = 0.635$

Step6: Calculate upper limit

$UL=2.61+1.5\times0.79=2.61 + 1.185=3.795$

Step7: Recall formula for variance

The variance $s^{2}$ is the square of the standard deviation $s$. Given $s = 0.45$, then $s^{2}=0.45^{2}=0.2025$

Answer:

(g) $0.79$
(h) LL: $0.635$, UL: $3.795$
(i) $0.2025$