Answer:
(a) Mean and Median of type A
[tex]\bar x = 2145.47[/tex]
[tex]Median = 966[/tex]
(b) Mean and Median of type B
[tex]\bar x = 531.73[/tex]
[tex]Median = 366[/tex]
(c) The claim by the public health worker is true.
Step-by-step explanation:
Given
[tex]Type\ A: 38\ 100\ 186\ 199\ 253\ 380\ 595\ 966\ 1611\ 2638\ 3845\ 4931\ 5183\ 5367\ 5890[/tex]
[tex]Type\ B: 59\ 95\ 116\ 143\ 156\ 225\ 271\ 366\ 495\ 696\ 851\ 1060\ 1140\ 1101\ 1202[/tex]
[tex]n = 15[/tex]
Solving (a): The mean and median of A.
Mean is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{38 +100 +186 +199+ 253+ 380+ 595+ 966 +1611 +2638 +3845+ 4931+ 5183 +5367 +5890 }{15}[/tex]
[tex]\bar x = \frac{32182}{15}[/tex]
[tex]\bar x = 2145.47[/tex]
The median is calculated using:
[tex]Median = \frac{n+1}{2}th[/tex]
[tex]Median = \frac{15+1}{2}th[/tex]
[tex]Median = \frac{16}{2}th[/tex]
[tex]Median = 8th[/tex]
The 8th item is: 966
So:
[tex]Median = 966[/tex]
Solving (b): The mean and median of B.
Mean is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{59 +95 +116+ 143+ 156+ 225+ 271+ 366+ 495 +696+ 851+ 1060+ 1140 +1101+ 1202}{15}[/tex]
[tex]\bar x = \frac{7976}{15}[/tex]
[tex]\bar x = 531.73[/tex]
The median is calculated using:
[tex]Median = \frac{n+1}{2}th[/tex]
[tex]Median = \frac{15+1}{2}th[/tex]
[tex]Median = \frac{16}{2}th[/tex]
[tex]Median = 8th[/tex]
The 8th item is: 366
So:
[tex]Median = 366[/tex]
(c) The claim by the public health worker is true.
To do this, we simply compare the mean value of both types.
For Type A
[tex]\bar x = 2145.47[/tex]
For Type B
[tex]\bar x = 531.73[/tex]
The claim is:
[tex]Type\ A > 2 * Type B[/tex]
[tex]2145.47 > 2 * 531.73[/tex]
[tex]2145.47 > 1063.46[/tex]
Since the inequality is true, then the claim is true
