Find the mean of 4, 10, 5, 8, 1, 8 graphically.
What is the sum of the numbers?
To find the mean graphically, we first add up all the numbers:
4 + 10 + 5 + 8 + 1 + 8 = 36
Next, we represent each number as a point on a number line, with a dot at the location corresponding to the value of the number. For example, the point representing the number 4 would be located four units to the right of 0 on the number line.
Once we have represented all the numbers in this way, we find the midpoint of the line segment connecting the first and last points. This midpoint represents the mean of the numbers.
Since we have six numbers, representing them on a number line gets crowded and difficult to represent. But following the steps, we can easily evaluate the mean graphically.
Sum of the numbers = 36
Mean of the numbers:
First of all, we find the range of the data = maximum value - minimum value
= 10 - 1
= 9
Now, we divide this range into equal parts - one part for each value in the data. To do this, we divide the range into 6 equal parts (since we have 6 numbers) by adding the common difference to the minimum value repeatedly:
1, 1 + 9/6, 1 + 2(9/6), 1 + 3(9/6), 1 + 4(9/6), 1 + 5(9/6)
= 1, 2.5, 4, 5.5, 7, 8.5
Now, we represent each of the data values using points on the number line, as shown below:
1 4 5 8 8 10
o----o---o-----o--o-----o
| | | | | |
1 2.5 4 5.5 7 8.5
Finally, we find the midpoint of the line segment connecting the first and last points:
1 4 5 8 8 10
o----o---o-----o--o-----o
| | | | | |
1 2.5 4 5.5 7 8.5
-
|
6th part
The midpoint is at:
midpoint = (5 + 7) / 2 = 6
Therefore, the mean of the data is 6.
Sum of the numbers is 36.
To find the mean of a set of numbers graphically, you need to create a bar graph representing the data. Let's start by graphing the numbers:
1: █
4: ████
5: ███
8: ██████
8: ██████
10: ██████████
Next, we calculate the sum of the numbers:
1 + 4 + 5 + 8 + 8 + 10 = 36
So, the sum of the numbers is 36.