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Question
A study of the yield of 150 tomato plants, resulted in the record:
| Tomatoes per Plant | 1 - 5 | 6 - 10 | 11 - 15 | 16 - 20 | 21 - 25 |
| Number of Plants | 20 | 50 | 46 | 22 | 12 |
What is the frequency of the class preceding the modal class?
Solution
| Tomatoes per Plant | Mid-Point (x) | Number of Plants (f) | fx |
| 1 - 5 | 3 | 20 | 60 |
| 6 - 10 | 8 | 50 | 400 |
| 11 - 15 | 13 | 46 | 598 |
| 16 - 20 | 18 | 22 | 396 |
| 21 - 25 | 23 | 12 | 276 |
| Total | 150 | 1730 |
The frequency of the class preceding the modal class is 20.
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RELATED QUESTIONS
The following table shows the ages of the patients admitted in a hospital during a year:
| Age (in years) | 5 − 15 | 15 − 25 | 25 − 35 | 35 − 45 | 45 − 55 | 55 − 65 |
| Number of patients | 6 | 11 | 21 | 23 | 14 | 5 |
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:
| Lifetimes (in hours) | 0 − 20 | 20 − 40 | 40 − 60 | 60 − 80 | 80 − 100 | 100− 120 |
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The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.
| Monthly consumption (in units) | Number of consumers |
| 65 - 85 | 4 |
| 85 - 105 | 5 |
| 105 - 125 | 13 |
| 125 - 145 | 20 |
| 145 - 165 | 14 |
| 165 - 185 | 8 |
| 185 - 205 | 4 |
The following table gives the daily income of 50 workers of a factory:
| Daily income (in Rs) | 100 - 120 | 120 - 140 | 140 - 160 | 160 - 180 | 180 - 200 |
| Number of workers: | 12 | 14 | 8 | 6 | 10 |
Find the mean, mode and median of the above data.
Compute the mode from the following data:
| Class interval | 1 – 5 | 6 – 10 | 11 – 15 | 16 – 20 | 21 – 25 | 26 – 30 | 31 – 35 | 36 – 40 | 41 – 45 | 46 – 50 |
| Frequency | 3 | 8 | 13 | 18 | 28 | 20 | 13 | 8 | 6 | 4 |
Find out the mode from the following data:
| Wages (in ₹) | No. of persons |
| 125 | 3 |
| 175 | 8 |
| 225 | 21 |
| 275 | 6 |
| 325 | 4 |
| 375 | 2 |
Find the mode of the following frequency distribution:
| x | 10 | 11 | 12 | 13 | 14 | 15 |
| f | 1 | 4 | 7 | 5 | 9 | 3 |
The monthly salary of 10 employees in a factory are given below:
₹ 5000, ₹ 7000, ₹ 5000, ₹ 7000, ₹ 8000, ₹ 7000, ₹ 7000, ₹ 8000, ₹ 7000, ₹ 5000
Find the mean, median and mode
Find the mode of the following data:
| Marks | 0 − 10 | 10 − 20 | 20 − 30 | 30 − 40 | 40 − 50 |
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The following frequency distribution table shows the classification of the number of vehicles and the volume of petrol filled in them. To find the mode of the volume of petrol filled, complete the following activity:
| Class (Petrol filled in Liters) |
Frequency (Number of Vehicles) |
| 0.5 - 3.5 | 33 |
| 3.5 - 6.5 | 40 |
| 6.5 - 9.5 | 27 |
| 9.5 - 12.5 | 18 |
| 12.5 - 15.5 | 12 |
Activity:
From the given table,
Modal class = `square`
∴ Mode = `square + [(f_1 - f_0)/(2f_1 -f_0 - square)] xx h`
∴ Mode = `3.5 + [(40 - 33)/(2(40) - 33 - 27)] xx square`
∴ Mode = `3.5 +[7/(80 - 60)] xx 3`
∴ Mode = `square`
∴ The mode of the volume of petrol filled is `square`.
