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Question
250 apples of a box were weighed and the distribution of masses of the apples is given in the following table:
| Mass (in grams) |
80 – 100 | 100 – 120 | 120 – 140 | 140 – 160 | 160 – 180 |
| Number of apples |
20 | 60 | 70 | x | 60 |
Find the modal mass of the apples.
Solution
Mode = `l + (f_1 - f_0)/(2f_1 - f_0 - f_2) xx h` ...(1)
Where l = lower class limit of modal class = 12
Modal class is (120 – 140), Since it consists highest frequency
∴ l = 120
h = class size = 20
f1 = frequency of modal class = 70
f0 = frequency of class preceding the modal class = 60
f2 = frequency of class succeeding the modal class = 40
On putting these values in (1), we get
Modal mass or mode
= `120 + ((70 - 60)/(2 xx 70 - 60 - 40)) xx 20`
= `120 + 10/40 xx 20`
= `120 + 10/2`
= 120 + 5
= 125
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.
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data.
| Number of cars | 0 − 10 | 10 − 20 | 20 − 30 | 30 − 40 | 40 − 50 | 50 − 60 | 60 − 70 | 70 − 80 |
| Frequency | 7 | 14 | 13 | 12 | 20 | 11 | 15 | 8 |
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 |
Find the mean, median and mode of the following data:
| Classes: | 0-20 | 20-40 | 40-60 | 40-60 | 80-100 | 100-120 | 120-140 |
| Frequency: | 6 | 8 | 10 | 12 | 6 | 5 | 3 |
Find the mode of the following distribution:
| Marks | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 |
| Frequency | 12 | 35 | 45 | 25 | 13 |
Heights of students of class X are givee in the flowing frequency distribution
| Height (in cm) | 150 – 155 | 155 – 160 | 160 – 165 | 165 – 170 | 170 - 175 |
| Number of students | 15 | 8 | 20 | 12 | 5 |
Find the modal height.
Also, find the mean height. Compared and interpret the two measures of central tendency.
Find the mode of the following data.
| Class interval | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
| Frequency | 7 | 13 | 14 | 5 | 11 |
From one footwear shop, 12 pairs of chappals were sold. The sizes of these chappals are given below.
7, 8, 6, 7, 7, 5, 9, 7, 6, 7, 8, 7
Find their mode.
The upper limit of the modal class of the given distribution is:
| Height [in cm] | Below 140 | Below 145 | Below 150 | Below 155 | Below 160 | Below 165 |
| Number of girls | 4 | 11 | 29 | 40 | 46 | 51 |
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`.
