Mean Mode and Median
Mean, Mode and Median
Ungrouped and Grouped Data
Ungrouped Data refers to raw data that has been ‘processed’; so as to determine frequencies. The data, along with the frequencies, are presented individually.
Grouped Data refers to values that have been analysed and arranged into groups called ‘class’. The classes are based on intervals – the range of values – being used.
It is from these classes, are upper and lower class boundaries found.
Mean
Mean
The
‘Mean’ is the total of all the values in the set of data divided by the total number of values in a set of data.
The arithmetic mean (or simply "mean") of a sample is the sum the sampled values divided by the number of items in the sample.
x is the value of a member of the set of data
f is the frequency or number of members of the set of data
Mean=
Therefore: = 6.56
Grades
Frequency (f)
Total Value (x)
1
5
5
2
2
4
3
7
21
4
4
16
5
4
20
6
1
6
7
8
56
8
3
24
9
5
45
10
4
40
11
4
44
12
5
60
TOTALS
52
341
Mean in relation to Grouped Data
Mean in relation to grouped data emphasizes the usage of class intervals. Rather than the data being presented individually, they are presented in groupings (called class). It is from there a midpoint is
Grade
Intervals
Frequency (f)
1-3
14
4-6
9
7-9
16
10-12
13
reached (for each interval).
Unlike Ungrouped data, the mean is estimated using the intervals. It will prove difficult to gain the most accurate mean.
Mean in relation to Grouped Data
There several things we must acknowledge before we determine the mean.
They are:
1.
Interval width – the number of values in each interval.
2.
Lower class boundaries – the lowest value in each interval.
3.
Upper class boundaries – the highest value in each interval.
4.
Midpoints – the halfway point between the values of each interval.
Keeping all these things in mind, focus on the midpoint. The midpoint is what we must use to estimate the mean.
Mean in relation to
Ungrouped and Grouped Data
Ungrouped Data refers to raw data that has been ‘processed’; so as to determine frequencies. The data, along with the frequencies, are presented individually.
Grouped Data refers to values that have been analysed and arranged into groups called ‘class’. The classes are based on intervals – the range of values – being used.
It is from these classes, are upper and lower class boundaries found.
Mean
Mean
The
‘Mean’ is the total of all the values in the set of data divided by the total number of values in a set of data.
The arithmetic mean (or simply "mean") of a sample is the sum the sampled values divided by the number of items in the sample.
x is the value of a member of the set of data
f is the frequency or number of members of the set of data
Mean=
Therefore: = 6.56
Grades
Frequency (f)
Total Value (x)
1
5
5
2
2
4
3
7
21
4
4
16
5
4
20
6
1
6
7
8
56
8
3
24
9
5
45
10
4
40
11
4
44
12
5
60
TOTALS
52
341
Mean in relation to Grouped Data
Mean in relation to grouped data emphasizes the usage of class intervals. Rather than the data being presented individually, they are presented in groupings (called class). It is from there a midpoint is
Grade
Intervals
Frequency (f)
1-3
14
4-6
9
7-9
16
10-12
13
reached (for each interval).
Unlike Ungrouped data, the mean is estimated using the intervals. It will prove difficult to gain the most accurate mean.
Mean in relation to Grouped Data
There several things we must acknowledge before we determine the mean.
They are:
1.
Interval width – the number of values in each interval.
2.
Lower class boundaries – the lowest value in each interval.
3.
Upper class boundaries – the highest value in each interval.
4.
Midpoints – the halfway point between the values of each interval.
Keeping all these things in mind, focus on the midpoint. The midpoint is what we must use to estimate the mean.
Mean in relation to