Finding Averages from Frequency Tables

1
Finding Averages from Frequency Tables
Here is the data from a survey of girls shoe sizes
To find the mode we look for the most common
6
To find the median we look for the middle number
when put in order of size
5
To find the mean we add them together and divide
by how many there are
4.7
But we can make the calculation easier by putting
it the data into a frequency table
2
Finding Averages from Frequency Tables
2
2
2
3
3
3
3
4
4
4
4
4
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
7
7
How a frequency table is made
3
6
4
12
5
20
7
35
9
54
14
2
Shoe size 2,
3 pieces of data,
add them together
2 2 2
or 2 x 3
Shoe size 3,
4 pieces of data,
add them together
3 3 3 3
or 3 x 4
or 4 x 5
Shoe size 4,
5 pieces of data,
add them together
4 4 4 4 4
or 5 x 7
Shoe size 5,
7 pieces of data,
add them together
5 5 5 5 5 5 5
Shoe size 6,
9 pieces of data,
add them together
6 6 6 6 6 6 6 6 6
or 6 x 9
Shoe size 7
2 pieces of data
add them together
7 7
or 7 x 2
3
Finding Averages from Frequency Tables
To calculate the mean we need to know what is the
total and how many there are
So the mean is
141 30
4.7
What is the total of all the data added together?
4
Finding Averages from Frequency Tables
To find the mode we look for the most frequently
appearing value in other words the largest
frequency
because the shoe size 6 has the highest frequency
(or there are more 6s than any other number)
shoe size 6 is the modal size
mode 6
5
Make a running total of the position number at
the end of each data group.
Finding Averages from Frequency Tables
3
7
12
19
The median is the middle value when all the data
is placed in order of size (usually smallest to
largest).
The 15th and 16th values Are in the Shoe size
5 Group so 5 is the median
In a frequency table the values are already in
order of size
To find the position of the middle value we add 1
to the total frequency and half it
30 1 2
15.5
The middle position is halfway between 15 and 16
Where is this in the table?
6
Finding Averages from Frequency Tables
Now find the mean mode and median for this
frequency table
Mode 4
(highest frequency)
2
1
6
3
16
7
15
In the 4 group
15
Median 4
54
12
54
4.5
12