Question

question #3
the front row of a movie theater has 23 seats. if you sit in the seat that is located in the median position, in which seat would you be seated?
12
1
23
11

question #4
which data set has a mean of 18, a median of 18, and a mode of 18?
11, 13, 14, 19, 19, 20, 21, 23, 25, 28
12, 12, 13, 13, 14, 14, 18, 18, 18, 18
12, 13, 15, 18, 18, 18, 19, 21, 24, 26
12, 13, 15, 17, 18, 18, 19, 20, 23, 25

Explanation:

Step1: Find the median position formula

For a set of \(n\) values, if \(n\) is odd, the median position is \(\frac{n + 1}{2}\). Here \(n=23\).

Step2: Calculate the median position

Substitute \(n = 23\) into \(\frac{n+1}{2}\), we get \(\frac{23 + 1}{2}=\frac{24}{2}=12\).

Step1: Calculate the mean

For the data set \(12,13,15,18,18,18,19,21,24,26\):
The sum is \(12+13+15+18+18+18+19+21+24+26 = 184\).
The mean is \(\frac{184}{10}=18.4\) (incorrect for question 4).
For \(12,12,13,13,14,14,18,18,18,18\):
Sum is \(12\times2 + 13\times2+14\times2+18\times4=24 + 26+28 + 72=150\), mean is \(\frac{150}{10}=15\) (incorrect).
For \(12,13,15,17,18,18,19,20,23,25\):
Sum is \(12+13+15+17+18+18+19+20+23+25=180\), mean is \(\frac{180}{10} = 18\).
Median: Arrange the data \(12,13,15,17,18,18,19,20,23,25\). The median of \(n = 10\) (even) is \(\frac{5^{th}+6^{th}}{2}=\frac{18 + 18}{2}=18\).
Mode: The most - frequent value is \(18\).

Answer:

12