Answer:
(a)
Step-by-step explanation:
Given
See attachment for sets A and B
Required
The true statement about both sets
First, we calculate the typical values (mean) of set A and set B.
This is calculated as:
[tex]Mean = \frac{\sum fx}{\sum f}[/tex]
For A:
[tex]A= \frac{0*1+2*1+5*1+6*1+7*1}{1+1+1+1+1}[/tex]
[tex]A= \frac{20}{5}[/tex]
[tex]A =4[/tex]
For B:
[tex]B = \frac{7 * 1 + 8 *1 + 9 * 2 + 10 * 1}{1+1+2+1}[/tex]
[tex]B = \frac{43}{5}[/tex]
[tex]B = 8.6[/tex]
Here, we can conclude that B has a larger typical value
Next calculate the spread (range) of sets A and B
This is calculated as:
[tex]Range = Highest -Least[/tex]
For A:
[tex]A = 7 - 0[/tex]
[tex]A = 7[/tex]
For B
[tex]B=10 - 7[/tex]
[tex]B = 3[/tex]
Here, we can conclude that A has a larger spread.
Hence, (a) is true
