Answer:
D. [tex]Q_3=47[/tex]
Step-by-step explanation:
We have been given a table that represents the the number of electoral votes California was assigned each decade of the past century. We are asked to find the 3rd quartile of our given data.
The number of votes are: 9, 13, 13, 22, 25, 32, 40, 45, 47, 54, 55.
We will use upper quartile formula to solve our given problem.
[tex]Q_3=\frac{3}{4}*(n+1)^{\text{th term}}[/tex], where, n represents the number of elements in the data set.
We can see that our data set has 11 data points, so upon substituting n=11 in above formula we will get,
[tex]Q_3=\frac{3}{4}*(11+1)^{\text{th term}}[/tex]
[tex]Q_3=\frac{3}{4}*(12)^{\text{th term}}[/tex]
[tex]Q_3=3*3^{\text{th term}}[/tex]
[tex]Q_3=9^{\text{th term}}[/tex]
Now let us count 9th term of our data set. Upon counting our data set from left to right we can see that 9th term of our data set is 47, therefore, 3rd quartile of our given data is 47 and option D is the correct choice.
