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Mode using Grouping Method Example-4
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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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5. Example-4
Calculate Mode using Grouping Method from the following grouped data
| Class | Frequency | | 10 - 20 | 4 | | 20 - 30 | 6 | | 30 - 40 | 5 | | 40 - 50 | 10 | | 50 - 60 | 20 | | 60 - 70 | 22 | | 70 - 80 | 24 | | 80 - 90 | 6 | | 90 - 100 | 3 |
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 :
| Class | I
Frequency | II
(1+2) | III
(2+3) | IV
(1+2+3) | V
(2+3+4) | VI
(3+4+5) | | 10-20 | 4 | | | | | | | | 4+6=10 | | | | | | 20-30 | 6 | | | 4+6+5=15 | | | | | | 6+5=11 | | | | | 30-40 | 5 | | | | 6+5+10=21 | | | | 5+10=15 | | | | | | 40-50 | 10 | | | | | 5+10+20=35 | | | | 10+20=30 | | | | | 50-60 | 20 | | | 10+20+22=52 | | | | | 20+22=42 | | | | | | 60-70 | 22 | | | | 20+22+24=66 | | | | | 22+24=46 | | | | | 70-80 | 24 | | | | | 22+24+6=52 | | | 24+6=30 | | | | | | 80-90 | 6 | | | 24+6+3=33 | | | | | | 6+3=9 | | | | | 90-100 | 3 | | | | | |
1) 24 is the maximum value in the column-I and it is an individual frequency of Class 70-80. Therefore, we have tick(✓) this Class.
2) 42 is the maximum value in the column-II and it is the sum of 20 and 22; i.e., of Class 50-60 and 60-70. Therefore, we have tick(✓) this both Class.
3) 46 is the maximum value in the column-III and it is the sum of 22 and 24; i.e., of Class 60-70 and 70-80. Therefore, we have tick(✓) this both Class.
4) 52 is the maximum value in the column-IV and it is the sum of 10, 20, and 22; i.e, of Class 40-50, 50-60 and 60-70. Therefore, we have tick(✓) this three Class.
5) 66 is the maximum value in the column-V and it is the sum of 20, 22, and 24; i.e, of Class 50-60, 60-70 and 70-80. Therefore, we have tick(✓) this three Class.
6) 52 is the maximum value in the column-VI and it is the sum of 22, 24, and 6; i.e, of Class 60-70, 70-80 and 80-90. Therefore, we have tick(✓) this three Class.
Analysis Table :
| Column | I | II | III | IV | V | VI | Total | | Max Frequency | 24 | 42 | 46 | 52 | 66 | 52 | | | 10-20 | | | | | | | - | | 20-30 | | | | | | | - | | 30-40 | | | | | | | - | | 40-50 | | | | ✓ | | | 1 | | 50-60 | | ✓ | | ✓ | ✓ | | 3 | | 60-70 | | ✓ | ✓ | ✓ | ✓ | ✓ | 5 | | 70-80 | ✓ | | ✓ | | ✓ | ✓ | 4 | | 80-90 | | | | | | ✓ | 1 | | 90-100 | | | | | | | - |
Since 60-70 has the maximum ticks 5. So mode class is 60-70.
`:.` The mode class is `60 - 70`.
`:. L = `lower boundary point of mode class `=60`
`:. f_1 = ` frequency of the mode class `=22`
`:. f_0 = ` frequency of the preceding class `=20`
`:. f_2 = ` frequency of the succedding class `=24`
`:. c = ` class length of mode class `=10`
`Z=L+(|f_1-f_0|)/(|f_1-f_0|+|f_1-f_2|) * c`
`=60+(|22-20|)/(|22-20| + |22-24|) * 10`
`=60+2/4 * 10`
`=60+5`
`=65`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
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