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प्रश्न
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 |
उत्तर
From the given data, it can be observed that the maximum class frequency is 20, belonging to 40 − 50 class intervals.
Therefore, modal class = 40 − 50
Lower limit (l) of modal class = 40
Frequency (f1) of modal class = 20
Frequency (f0) of class preceding modal class = 12
Frequency (f2) of class succeeding modal class = 11
Class size = 10
`"Mode" = l + ((f_1-f_0)/(2f_1-f_0-f_2))xxh`
= `40+[(20-12)/(2(20)-12-11)]xx10`
= `40+((80)/(40-23))`
= 40 + 4.7
= 44.7
Therefore, the mode of this data is 44.7 cars.
संबंधित प्रश्न
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 mode of the following data:
15, 8, 26, 25, 24, 15, 18, 20, 24, 15, 19, 15
Find the mode of the following distribution.
| Class-interval: | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |
| Frequency: | 5 | 8 | 7 | 12 | 28 | 20 | 10 | 10 |
The following is the distribution of height of students of a certain class in a certain city:
| Height (in cm): | 160 - 162 | 163 - 165 | 166 - 168 | 169 - 171 | 172 - 174 |
| No. of students: | 15 | 118 | 142 | 127 | 18 |
Find the average height of maximum number of students.
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 |
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.
Find the mode of the following distribution:
| Marks | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 |
| Frequency | 12 | 35 | 45 | 25 | 13 |
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 |
The frequency distribution for agriculture holdings in a village is given below:
| Area of land (in hectares) | 1 – 3 | 3 – 5 | 5 – 7 | 7 – 9 | 9 – 11 | 11 – 13 |
| Number of families | 20 | 45 | 80 | 55 | 40 | 12 |
Find the modal agriculture holding per family.
If mode of a series exceeds its mean by 12, then mode exceeds the median by
Find the mode of the following frequency distribution:
| x | 10 | 11 | 12 | 13 | 14 | 15 |
| f | 1 | 4 | 7 | 5 | 9 | 3 |
The following table give the marks scored by students in an examination:
| Marks | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 |
| No. of students | 3 | 7 | 15 | 24 | 16 | 8 | 5 | 2 |
(i) Find the modal group
(ii) Which group has the least frequency?
For the data 11, 15, 17, x + 1, 19, x – 2, 3 if the mean is 14, find the value of x. Also find the mode of the data
In the formula `x-a+(sumf_i d_i)/(sumf_i),` for finding the mean of grouped data d1's are deviations from the ______.
If xi's are the midpoints of the class intervals of grouped data, fi's are the corresponding frequencies and `barx` is the mean, then `sum(f_ix_i-barx)` is equal to ______.
Construction of a cumulative frequency table is useful in determining the ______.
The mode of the following data is:
| xi | 10 | 14 | 18 | 21 | 25 |
| fi | 10 | 15 | 7 | 9 | 9 |
There are lottery tickets labelled numbers from 1 to 500. I want to find the number which is most common in the lottery tickets. What quantity do I need to use?
Mrs. Garg recorded the marks obtained by her students in the following table. She calculated the modal marks of the students of the class as 45. While printing the data, a blank was left. Find the missing frequency in the table given below.
| Marks Obtained |
0 − 20 | 20 − 40 | 40 − 60 | 60 − 80 | 80 − 100 |
| Number of Students |
5 | 10 | − | 6 | 3 |
For the following distribution:
| Class | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 |
| Frequency | 10 | 15 | 12 | 20 | 9 |
The lower limit of modal class is:
