Video Transcript
The histogram shows the ages of 25 children in a swimming pool on a Saturday morning. Use the histogram to find which of the following is the average, the arithmetic mean, age of the 25 children. A) Six, B) seven, C) four, or D) five.
In this histogram along the 𝑥-axis, we have the ages of the children. And along the 𝑦-axis, we have the number of children that were the specified ages. But before we can use this information, we have to remember what the average or the arithmetic mean is.
To find an average, we take the sum of all values and we divide that by the number of values we have. In this case, the average age will be equal to the sum of all 25 ages divided by 25. Looking back at our histogram, we see that for the age of three, the bar goes up to four on the 𝑦-axis. So we can say that four children were three. Now, we could write out three plus three plus three plus three and keep going and list out all 25 ages. However, there is a more reasonable way.
Since we know that there were four children who were three years old, we can multiply three times four and find a sum of 12 for the children that were aged three. Three plus itself four times is 12. Three times four is 12. When we move on to age four, it goes up to seven along the 𝑦-axis, seven children more four. If we multiply four times seven, we get 28. 28 is the sum of ages of all the four-year olds. Now, for age five, there were five children aged five. We multiply five times five. And we say the sum of the age of all five-year olds was 25. Six-year olds, we can see there were three. We multiply six times three. The sum of all the six-year olds will be 18. And finally, the seven-year olds, there were six seven-year olds. So we multiply seven times six, which is 42, the sum of the ages of all the seven-year olds together.
At this point, we have partial sums. We have the sums of the three-year olds, four-year olds, five-year olds, six-year olds, and seven-year olds. And we need to total these five values. When we add them together, we get 125. So we’ll have a fraction of 125 over 25. We know that 125 divided by 25 equals five.
And so, we can say that the average age of the children in the pool was five, option D.
