Mode
Mode or modal value is the value that occurs maximum times in a set of observations and around which the other items of set cluster densely.
In other words, we can say that it is that value of the variable which has maximum frequency.
Merits and Demerits of modal value
Example : Find the modal value of 23,25,23,45,23,41,25,23,46
From the given data we can see that 23 occurs maximum time so the modal value of the given data is 23.
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Example : Find the modal value of 123,132,145,176,180,120
From the above data we can see that no number is repeating, each observation is occurring only once so there is no modal value.
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Example : Find the modal value of 13, 15, 15, 13 ,16,18,15,13,17,14,14
Solution :
Observations |
Frequency |
13 |
3 |
14 |
2 |
15 |
3 |
16 |
1 |
17 |
1 |
18 |
1 |
So from the above table 13 and 15 are occurring maximum times so modal value is 13 and 15 both.
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Computation of modal value for continuous Frequency Distribution
First obtain the frequency distribution and determine the class of maximum frequency. That class will be the modal class. And then use the following formula to find the modal value.
Where , l = Lower limit of the modal class.
f = Frequency of the modal class.
h = width of the modal class.
f1 = Frequency of the class preceding the modal class.
f2 = Frequency of the class following the modal class.
Some solved examples
1) A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:
Family size |
1 - 3 |
3 - 5 |
5 - 7 |
7 - 9 |
9 - 11 |
Number of families(f) |
7 |
8 |
2 |
2 |
1 |
Solution :
Family size |
Number families |
1-3 |
7 ( f _{0}) |
3-5 |
8 (f _{1}) |
5-7 |
2 (f _{2}) |
7-9 |
2 |
9-11 |
1 |
Here maximum frequency class is 3-5. So,
Here, l = 3 , f
_{1} = 8 , f
_{0} = 7 and f
_{2} = 2
Mode = 3 + [ ( 8 – 7) / ( 2 x 8 -7 -2)] x 2
⇒ = 3 + ( 1 / 7 ) x 2
⇒ = 3 + 2 / 7
⇒ = 3 + 0.286
∴ Modal value = 3.286
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Relationship between Mean , Median and modal value
Mode = 3 Median – 2 Mean
Or Median = Modal value + 2 / 3 ( Mean – Modal value)
Or Mean = Modal value + 3 / 2 ( Median – Modal value) |
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Some solved examples
1) Given median = 22.6, mode = 28 Find mean.
Solution :
Modal value = 3 Median – 2 Mean
28 = 3 (22.6) – 2 Mean
28 = 67.8 – 2 Mean
∴ 2 Mean = 67.8 – 28
2 Mean = 39 .8
∴ Mean = 39.8 / 2 = 19.9
∴ Mean = 19.9
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2) If Median = 20 and Mean = 22.5, find modal value.
Solution :>BR?
Mode = 3 Median – 2 Mean
⇒ = 3 ( 20 ) – 2 (22.5)
⇒ = 60 – 45
∴ Modal value = 15
Statistics
• Statistics
• Pictograph
• Pie chart
• Bar Graph
• Double Bar Graph
• Histogram
• Frequency polygon
• Frequency distribution (Discrete )
• Frequency distribution continuous (or grouped)
• Measures of central tendency ( Mean, Mode and Median)
• Ogive or Frequency curve.
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