The mode is the value that occurs most frequently in a data set. A data set can have multiple modes if two or more values tie for most frequent. Mode is calculated by finding the most common value(s). Mode is easy to calculate but does not use all data points. Weighted mean assigns weights to values based on importance before calculating the average. The relationship between mean, median and mode indicates the symmetry or skew of a distribution.

1.  Mode:
The most repeated or most common or the
most frequent Value which occurs in a set of
values.
The mode is the value in a data set that
occur most frequently.
A set of data can have more than one mode
if two or more values tie for the most
frequently occurring value.

2.  Collect the sample data.
a sample of 20 group was selected at
random.
2,4,1,2,3,2,4,2,3,6,8,4,2,1,7,4,2,4,4,3.
“most repeated value or values” Mode = 2,4
X Frequency
1 2
2 6
3 3
4 6
5 0
6 1
7 1
8 1

3.  For group data
Mode = l + (fm – f1) * h
(fm- f1) + (fm –f2)
here
l = lower limit class boundary of the mode
group
fm= maximum frequency
f1 = frequency preceding the fm
f2 = frequency following the fm
h = class interval

4. Marks F Class boundary
30 - 39 2 29.5 – 39.5
40 – 49 3 39.5 – 49.5
50 – 59 11 49.5 – 59.5
60 – 69 20 f1 59.5 – 69.5
70 – 79 32 fm l 69.5 – 79.5 mode
group
80- 89 25 f2 79.5 – 89.5
90 - 99 7 90.5 – 99.5

5. Mode = l + (fm – f1) * h
(fm- f1) + (fm –f2)
= 69.5 + ( 32 – 20) * 10
(32 – 20) + (32 – 25)
= 69.5 + 120
12+7
mode = 69.5 + 6.32 = 75.82

6.  Advantages:
1. It is easy and quick to calculate.
2. It is easy to understand.
3. Extreme values do not effect its values.
4. It can be determined from open end distribution.
5. It can be found by inspection from ungroup data.
6. It can be used for qualitative data.

7.  Disadvantage:
1. It is not well defined.
2. It is not based on all the observation of a set of
data.
3. It can not be used for further mathematical
processing.
4. There may be more then one value of the mode
in the set of data.
5. There may be no mode, if there is no common
value in the data.

8.  Weighted Mean:
weighted mean is a special case of arithmetic mean.
The mean value of data values that have been weighted
according to their relative importance.
 when the value are not equal importance, we assign
them certain numerical values to express their relative
importance. These numerical values are called
weights.
 Weighted mean =  WX / W

9.  The marks obtained by a students in English, Urdu
and Statistics were 70, 76 and 82 respectively.
Find the suitable average if weights of 5, 4 and 3
are assigned to these subjects.
 Weighted mean =  WX / W
= 5*70+4*76+3*82
5+4+3
= 900/12 = 75

10.  Empirical Relationship among Mean, Median and
Mode.
1. If Mean = Median = Mode then distribution is
symmetrical.
2. If Mean > Median > Mode then distribution is
positively skewed.
3. If Mean < Median < Mode then distribution is
negatively Skewed.