Chapter 1.4, Problem 69SR

To determine

To find: The mean of the given data.

Answer to Problem 69SR

The median of the given data is $21:48$ .

Explanation of Solution

Given information:

The times for the first $8$ meets of the season of Blanca’s cross country is shown in table:

Cross Country
Meet	Time
1	22:31
2	22:21
3	21:48
4	22:01
5	21:48
6	20:56
7	20:34
8	20:15

Calculation:

Convert $m:s$ time into seconds with the formula $60m+s$ seconds.

Convert each time of meeting to seconds:

Time in minutes : seconds	Time in seconds
$22:31$	$1351$
$22:21$	$1341$
$21:48$	$1308$
$22:01$	$1321$
$21:48$	$1308$
$20:56$	$1256$
$20:34$	$1234$
$20:15$	$1215$

Arrange the given time in ascending order:

Time in minutes : seconds	Time in seconds
$20:15$	$1215$
$20:34$	$1234$
$20:56$	$1256$
$21:48$	$1308$
$21:48$	$1308$
$22:01$	$1321$
$22:21$	$1341$
$22:31$	$1351$

The median of the data of $8$ observations is the mean of the fourth and fifth observation.

  $\begin{array}{c}\text{Median}=\frac{1308+1308}{2}\\ =1308\end{array}$

So, the median of the data in seconds is $1308$ seconds nearly.The value $1308$ seconds is equal to $21:48$ .

Therefore, the median of the given data is $21:48$ .