Question

The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. The results are shown below.

24 26 24 27
27 24 29 26
34 30 30 28
23 30 24 19
14 26 26 26
Find the median number of vehicles going through the line in a 15-minute period.
A: 27 vehicles B: 25.85 vehicles C: 30 vehicles D: 26 vehicles

Answer 1

The correct answer is: Option D: 26 vehicles

Explanation:

Median is the middle value of a sorted data set.

The formula for median depends on the number of values in the dataset.

First of all we have to arrange the given data in order

So,

14 19 23 24 24 24 24 26 26 26 26 26 27 27 28 29 30 30 30 34

Counting the values in the dataset

n = 20

As the number of values is even, the formula for median will be

`M = (1)/(2)((n)/(2)th\ value+((n)/(2)+1)th\ value)`

Putting the values

`M = (1)/(2)((20)/(2)th\ value+((20)/(2)+1)th\ value)\\M=(1)/(2)(10th\ value +[10+1]th\ value]\\M= (1)/(2)(10th\ value + 11th\ value)`

The 10th value in dataset is 26 and 11th is also 26 so

`M = (1)/(2)(26+26)\\M = (1)/(2)(52)\\M = 26`

Hence,

The correct answer is: Option D: 26 vehicles