What is the upper quartile, Q3, of the following data set? 54, 53, 46, 60, 62, 70, 43, 67, 48, 65, 55, 38, 52, 56, 41
scZoUnD [109]
The original data set is
{<span>54, 53, 46, 60, 62, 70, 43, 67, 48, 65, 55, 38, 52, 56, 41}
Sort the data values from smallest to largest to get
</span><span>{38, 41, 43, 46, 48, 52, 53, 54, 55, 56, 60, 62, 65, 67, 70}
</span>
Now find the middle most value. This is the value in the 8th slot. The first 7 values are below the median. The 8th value is the median itself. The next 7 values are above the median.
The value in the 8th slot is 54, so this is the median
Divide the sorted data set into two lists. I'll call them L and U
L = {<span>38, 41, 43, 46, 48, 52, 53}
U = {</span><span>55, 56, 60, 62, 65, 67, 70}
they each have 7 items. The list L is the lower half of the sorted data and U is the upper half. The split happens at the original median (54).
Q3 will be equal to the median of the list U
The median of U = </span>{<span>55, 56, 60, 62, 65, 67, 70} is 62 since it's the middle most value.
Therefore, Q3 = 62
Answer: 62</span>
let's analyze each case to determine the solution
<u>case 1)</u> f(0) = 2 and g(–2) = 0
For x=0-----> find the value of f(0) in the graph-----> f(0)=4
For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0
therefore
the statement of the case 1) is false
<u>case 2)</u> f(0) = 4 and g(–2) = 4
For x=0-----> find the value of f(0) in the graph-----> f(0)=4
For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0
therefore
the statement of the case 2) is false
<u>case 3)</u> f(2) = 0 and g(–2) = 0
For x=2-----> find the value of f(2) in the graph-----> f(2)=0
For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0
therefore
the statement of the case 3) is true
<u>case 4)</u> f(–2) = 0 and g(–2) = 0
For x=-2-----> find the value of f(-2) in the graph-----> f(-2) is greater than 12
For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0
therefore
the statement of the case 4) is false
therefore
<u>the answer is</u>
f(2) = 0 and g(–2) = 0-------> this statement is true
Step-by-step explanation:
ax2 + bx + c = 0
x12 = (-b ± √D) / 2a , D = b2 - 4ac .
5x2 + 7x + 3 = 0
a = 5 , b = 7 , c = 3
D = 49 - 60 = - 11 , x1 = (-7 - i √11) / 10
x2 = (-7 + i √11) / 10
