Question

1. what is the median of the following numbers?

10, 39, 71, 42, 39, 76, 38, 25
a. 42.5
b. 39
c. 42
d. 35.5

1. the front row in a movie theatre has 23 seats. if you were asked to sit in the seat that occupied the median position, in which seat would you have to sit?

a. 1
b. 11
c. 23
d. 12

1. what is the median score achieved by a student who recorded the following scores on 10 math quizzes?

68, 55, 70, 62, 71, 58, 81, 82, 63, 79
a. 68
b. 71
c. 69

Explanation:

Question 11

Step1: Sort the numbers

Sort \(10,39,71,42,39,76,38,25\) in ascending order: \(10,25,38,39,39,42,71,76\)

Step2: Find the median

Since there are \(n = 8\) numbers (even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th values. \(\frac{n}{2}=4\) and \(\frac{n}{2}+1 = 5\). The 4th value is \(39\) and the 5th value is \(39\). The median is \(\frac{39 + 39}{2}=39\)

Step1: Use the formula for median position

For \(n\) (odd number of data points), the median position is \(\frac{n + 1}{2}\). Here \(n=23\), so the median position is \(\frac{23+1}{2}=\frac{24}{2}=12\)

Step1: Sort the scores

Sort \(68,55,70,62,71,58,81,82,63,79\) in ascending order: \(55,58,62,63,68,70,71,79,81,82\)

Step2: Find the median

Since \(n = 10\) (even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=5\) and \(\frac{n}{2}+1=6\). The 5th value is \(68\) and the 6th value is \(70\). The median is \(\frac{68+70}{2}=69\)

Answer:

B. 39

Question 12