You can use statistics to summarise sets of data.
You can also use them to compare different sets of data.
You should already be able to calculate three different averages: the mode, the median, the mean.
Remember that the range is not an average. It measures how spread out a set of values or numbers is.
For a large set of data, it is not practical to list every number separately. Instead, you can record the data in a frequency table.
The mode is the most common value or number.
The median is the middle value, when they are listed in order.
The mean is the sum of all the values divided by the number of values.
The range is the largest value minus the smallest.
A frequency table is any table that records how often (frequently) data values occur.
WORKED EXAMPLE 10.1
Number of Beads
|
25
|
30
|
35
|
40
|
45
|
50
|
Frequency
|
34
|
48
|
61
|
30
|
15
|
12
|
The table shows the number of beads on 200 necklaces.
a. Find the mode.
- the mode is the number with the highest frequency. The number of beads of with the highest frequency in this table is 35. Therefore the mode is 35.
b. Find the mean.
- (25 x 34 + 30 x 48 + 35 x 61 + 40 x 30 + 45 x 15 + 50 x 12) ÷ the sum of all the frequencies. The sum of frequencies is: 34 + 48 + 61 + 30 + 15 + 12 = 200. Now that we know sum of frequencies, we can find the mean.
6900 ÷ 200 = 34.5
This is a reasonable answer because it is near the middle of all the possible number of beads.
c. Find the range.
The first step to find the range is to determine the largest and the smallest number of beads. In the table above, the largest number of beads is 50 and the smallest number of beads is 25. So, that'll be:
50 - 25 = 25.
the range is 25.
Another example..
Students spin coins until they get heads. They record their attempts in the table below.
50 - 25 = 25.
the range is 25.
Another example..
Students spin coins until they get heads. They record their attempts in the table below.
Students
|
Attempts
|
Caspar
|
1
|
Louise
|
3
|
Zoe
|
7
|
Alfie
|
6
|
Marcus
|
3
|
Joe
|
7
|
Jim
|
1
|
Bethany
|
9
|
Alexa
|
9
|
Anthony
|
3
|
Carly
|
2
|
Jack
|
2
|
Finn
|
4
|
Michelle
|
3
|
Tanya
|
8
|
a. Find the Mean: To find the mean, we must first count the total amount of attempts which is 68. And we have to count the number of students which is 15. We must then divide 68 by 15.
68 ÷ 15 = 4.5
So the mean is 4.5
b. Find the Median:
Median is the middle value when they are listed in orders. So we have to list the number of attempts in order first.
1,1,2,2,3,3,3,3,4,6,7,7,8,9,9
68 ÷ 15 = 4.5
So the mean is 4.5
b. Find the Median:
Median is the middle value when they are listed in orders. So we have to list the number of attempts in order first.
1,1,2,2,3,3,3,3,4,6,7,7,8,9,9
We have found that the middle value is 3, so the median is 3.
c. Find the Mode:
Mode is the most common value or number. From the data above we know that the most common number is 3. So the mode is 3.
d. Find the Range:
Range is the biggest value subtracted by the smallest value. In this case the biggest value is 9 and the smallest value is 1.
9 - 1 = 8
So the range is 8.
-pristina-
c. Find the Mode:
Mode is the most common value or number. From the data above we know that the most common number is 3. So the mode is 3.
d. Find the Range:
Range is the biggest value subtracted by the smallest value. In this case the biggest value is 9 and the smallest value is 1.
9 - 1 = 8
So the range is 8.
-pristina-
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