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Mode using Grouping Method Example-1
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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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2. Example-1
Calculate Mode using Grouping Method from the following grouped data
| X | Frequency | | 10 | 8 | | 15 | 12 | | 20 | 36 | | 25 | 35 | | 30 | 28 | | 35 | 18 | | 40 | 9 |
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 | 8 | | | | | | | | 8+12=20 | | | | | | 15 | 12 | | | 8+12+36=56 | | | | | | 12+36=48 | | | | | 20 | 36 | | | | 12+36+35=83 | | | | 36+35=71 | | | | | | 25 | 35 | | | | | 36+35+28=99 | | | | 35+28=63 | | | | | 30 | 28 | | | 35+28+18=81 | | | | | 28+18=46 | | | | | | 35 | 18 | | | | 28+18+9=55 | | | | | 18+9=27 | | | | | 40 | 9 | | | | | |
1) 36 is the maximum value in the column-I and it is an individual frequency of x 20. Therefore, we have tick(✓) this x.
2) 71 is the maximum value in the column-II and it is the sum of 36 and 35; i.e., of x 20 and 25. Therefore, we have tick(✓) this both x.
3) 63 is the maximum value in the column-III and it is the sum of 35 and 28; i.e., of x 25 and 30. Therefore, we have tick(✓) this both x.
4) 81 is the maximum value in the column-IV and it is the sum of 35, 28, and 18; i.e, of x 25, 30 and 35. Therefore, we have tick(✓) this three x.
5) 83 is the maximum value in the column-V and it is the sum of 12, 36, and 35; i.e, of x 15, 20 and 25. Therefore, we have tick(✓) this three x.
6) 99 is the maximum value in the column-VI and it is the sum of 36, 35, and 28; i.e, of x 20, 25 and 30. Therefore, we have tick(✓) this three x.
Analysis Table :
| Column | I | II | III | IV | V | VI | Total | | Max Frequency | 36 | 71 | 63 | 81 | 83 | 99 | | | 10 | | | | | | | - | | 15 | | | | | ✓ | | 1 | | 20 | ✓ | ✓ | | | ✓ | ✓ | 4 | | 25 | | ✓ | ✓ | ✓ | ✓ | ✓ | 5 | | 30 | | | ✓ | ✓ | | ✓ | 3 | | 35 | | | | ✓ | | | 1 | | 40 | | | | | | | - |
Since 25 has the maximum ticks 5. So mode is 25.
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
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