Question

1. the weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below. construct a box - plot for the data set. 310 320 450 460 470 500 520 540 580 600 650 700 710 840 870 900 1000 1200 1250 1300 1400 1720 2500 3700 a) 600 310 500 1200 3700 b) 500 310 700 1200 3700 c) 705 310 510 2225 3700 d) 510 310 705 1225 3700

Explanation:

Step1: Find the minimum value

The minimum value of the data - set $310,320,450,460,470,500,520,540,580,600,650,700,710,840,870,900,1000,1200,1250,1300,1400,1720,2500,3700$ is $310$.

Step2: Find the first - quartile ($Q_1$)

Since $n = 24$ (even), the position of $Q_1$ is $\frac{n + 1}{4}=\frac{24+1}{4}=6.25$. The first - quartile is the value between the 6th and 7th ordered data values. The 6th value is $500$ and the 7th value is $520$, so $Q_1=510$.

Step3: Find the median ($Q_2$)

The position of the median is $\frac{n}{2}=12$ and $\frac{n}{2}+1 = 13$. The median is the average of the 12th and 13th ordered data values. The 12th value is $700$ and the 13th value is $710$, so $Q_2 = 705$.

Step4: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(24 + 1)}{4}=18.75$. The third - quartile is the value between the 18th and 19th ordered data values. The 18th value is $1200$ and the 19th value is $1250$, so $Q_3=1225$.

Step5: Find the maximum value

The maximum value of the data - set is $3700$.

Answer:

D. 510, 705, 1225, 310, 3700