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Mode using Grouping Method Example-2
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- Formula
- Example-1
- Example-2
- Example-3
- Example-4
- Example-5
- Example-6
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Other related methods
- Mean, Median and Mode
- Quartile, Decile, Percentile, Octile, Quintile
- Population Variance, Standard deviation and coefficient of variation
- Sample Variance, Standard deviation and coefficient of variation
- Population Skewness, Kurtosis
- Sample Skewness, Kurtosis
- Geometric mean, Harmonic mean
- Mean deviation, Quartile deviation, Decile deviation, Percentile deviation
- Five number summary
- Box and Whisker Plots
- Mode using Grouping Method
- Less than type Cumulative frequency table
- More than type Cumulative frequency table
- Class and their frequency table
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3. Example-2
Calculate Mode using Grouping Method from the following grouped data
| X | Frequency | | 10 | 3 | | 20 | 5 | | 30 | 3 | | 40 | 1 | | 50 | 2 | | 60 | 5 | | 70 | 13 | | 80 | 9 | | 90 | 2 |
Solution:
Mode using Grouping Method :
1) In column-I, write the original frequency
2) In column-II, combine the frequency two by two, starting from top
3) In column-III, combine the frequency two by two, starting from second
4) In column-IV, combine the frequency three by three, starting from top
5) In column-V, combine the frequency three by three, starting from second
6) In column-VI, combine the frequency three by three, starting from third
Grouping Table :
| x | I
Frequency | II
(1+2) | III
(2+3) | IV
(1+2+3) | V
(2+3+4) | VI
(3+4+5) | | 10 | 3 | | | | | | | | 3+5=8 | | | | | | 20 | 5 | | | 3+5+3=11 | | | | | | 5+3=8 | | | | | 30 | 3 | | | | 5+3+1=9 | | | | 3+1=4 | | | | | | 40 | 1 | | | | | 3+1+2=6 | | | | 1+2=3 | | | | | 50 | 2 | | | 1+2+5=8 | | | | | 2+5=7 | | | | | | 60 | 5 | | | | 2+5+13=20 | | | | | 5+13=18 | | | | | 70 | 13 | | | | | 5+13+9=27 | | | 13+9=22 | | | | | | 80 | 9 | | | 13+9+2=24 | | | | | | 9+2=11 | | | | | 90 | 2 | | | | | |
1) 13 is the maximum value in the column-I and it is an individual frequency of x 70. Therefore, we have tick(✓) this x.
2) 22 is the maximum value in the column-II and it is the sum of 13 and 9; i.e., of x 70 and 80. Therefore, we have tick(✓) this both x.
3) 18 is the maximum value in the column-III and it is the sum of 5 and 13; i.e., of x 60 and 70. Therefore, we have tick(✓) this both x.
4) 24 is the maximum value in the column-IV and it is the sum of 13, 9, and 2; i.e, of x 70, 80 and 90. Therefore, we have tick(✓) this three x.
5) 20 is the maximum value in the column-V and it is the sum of 2, 5, and 13; i.e, of x 50, 60 and 70. Therefore, we have tick(✓) this three x.
6) 27 is the maximum value in the column-VI and it is the sum of 5, 13, and 9; i.e, of x 60, 70 and 80. Therefore, we have tick(✓) this three x.
Analysis Table :
| Column | I | II | III | IV | V | VI | Total | | Max Frequency | 13 | 22 | 18 | 24 | 20 | 27 | | | 10 | | | | | | | - | | 20 | | | | | | | - | | 30 | | | | | | | - | | 40 | | | | | | | - | | 50 | | | | | ✓ | | 1 | | 60 | | | ✓ | | ✓ | ✓ | 3 | | 70 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 6 | | 80 | | ✓ | | ✓ | | ✓ | 3 | | 90 | | | | ✓ | | | 1 |
Since 70 has the maximum ticks 6. So mode is 70.
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
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