b The median best represents the data. See solution.
Practice makes perfect
a Consider the given table.
Movie Lengths (Hours)
1 13
1 23
2
3
2 13
1 23
2
2
1 23
The given data set shows the lengths of nine movies. We will find the measures of center of the given data. Let's do one at a time.
Mean
The mean of a numerical data set is the sum of the data divided by the number of data values. In this case, the number of data values is 9. Therefore, we will divide the sum of the data by 9.
Therefore, the mean is 1 2627 hours, or about 1.96 hours.
Median
The median of a numerical data set is the middle number when the values are written in numerical order. If the data set has an even number of values, the mean of the two middle values will be the median. To find the median, let's write the given values in numerical order.
1 13, 1 23, 1 23, 1 23, 2, 2, 2, 2 13, 3
We can see that the median is 2 hours.
Mode
The mode of a data set is the value or values that occur most often. Let's take a look at the given values to find the mode.
1 13, 1 23, 1 23, 1 23, 2, 2, 2, 2 13, 3
Note that 1 23 and 2 are the most repeated values. Both of them occur three times. Therefore, the modes are 1 23 hours and 2 hours.
b In this part we are asked to find which measure of center best represents the data. Let's first recall the given data.
1 13, 1 23, 1 23, 1 23, 2, 2, 2, 2 13, 3
First, the mean 1 2627 is less than most of the values. Second, the modes 1 23 and 2 do not divide the data into equal groups. Finally, since the median 2 splits the data evenly, it best represents the data.
