The histogram above shows the distribution of the number of video games played by 20 high school students during one week. Which of the following is true for this group of 20 students?

1. The mean number of video games played is equal to the median number of video games played.
2. The mode number of video games played is equal to the median number of video games played.
3. The range of the number of video games played is 6.

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All of the stats can be gleamed from the histogram. To obtain the mean or arithmetic average, we need to find the the total number of video games played and divide it by the total number of students.

$$\text{Mean}=\left(\frac{0+9+4+6+5+6}{20}\right)$$ $$\text{Mean}=\frac{30}{20}$$ $$\text{Mean}=1.5$$

To find the median, we can count towards the middle number. Since there are 20 terms, we want to find the average of the 10^th and 11^th term.

In this case, both the 10^th and 11^th term is 1. Therefore,

$$\text{Median}=1$$

To find the mode, find the number with the highest frequency.

$$\text{Mode}=1$$

To find the range, simply take the largest number and subtract the smallest number.

$$\text{Range} = 6-0$$ $$\text{Range} = 6$$

It may be beneficial to convert the histogram into a simple list.

The list:

$$0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 6$$

Calculating mean, median, mode, and range:

$$\underbrace{0, 0, 0, 0, 0}_\text{$0\cdot5$}, \underbrace{1, 1, 1, 1, 1, 1, 1, 1, 1}_\text{$1\cdot 9$}, \underbrace{2, 2}_\text{$2\cdot 2$}, \underbrace{3, 3}_\text{$3\cdot 2$}, 5, 6$$ $$\text{Mean}=\left(\frac{0+9+4+6+5+6}{20}\right)$$ $$\text{Mean}=\frac{30}{20}$$ $$\text{Mean}=1.5$$

The median for 20 terms is the average of the 10^th and 11^th term. (Middle term for odd number of items)

$$0, 0, 0, 0, 0, 1, 1, 1, 1, \Large 1 \normalsize, \Large 1 \normalsize, 1, 1, 1, 2, 2, 3, 3, 5, 6$$ $$\text{Median}=1$$

The mode is the number that is present the most.

$$0, 0, 0, 0, 0, \colorbox{aqua}{1, 1, 1, 1, 1, 1, 1, 1, 1}, 2, 2, 3, 3, 5, 6$$ $$\text{Mode}=1$$ The range is the difference between the largest number and smallest number on the list. $$\Large 0 \normalsize, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 5, \Large 6$$ $$\text{Range}= 6-0$$ $$\text{Range}=6$$