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प्रश्न
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
| Runs scored | Number of batsmen |
| 3000 − 4000 | 4 |
| 4000 − 5000 | 18 |
| 5000 − 6000 | 9 |
| 6000 − 7000 | 7 |
| 7000 − 8000 | 6 |
| 8000 − 9000 | 3 |
| 9000 − 10000 | 1 |
| 10000 − 11000 | 1 |
Find the mode of the data.
उत्तर
From the given data, it can be observed that the maximum class frequency is 18, belonging to class interval 4000 − 5000.
Therefore, modal class = 4000 − 5000
Lower limit (l) of modal class = 4000
Frequency (f1) of modal class = 18
Frequency (f0) of class preceding modal class = 4
Frequency (f2) of class succeeding modal class = 9
Class size (h) = 1000
`"Mode" = l + ((f_1-f_0)/(2f_1-f_0-f_2))xxh`
= `4000+((18-4)/(2(18)-4-9))xx1000`
= `4000+(14000/23)`
= 4000 + 608.695
= 4608.695
Therefore, the mode of the given data is 4608.7 runs.
संबंधित 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 |
Find the mode of the following distribution.
| Class-interval: | 25 - 30 | 30 - 35 | 35 - 40 | 40 - 45 | 45 - 50 | 50 - 55 |
| Frequency: | 25 | 34 | 50 | 42 | 38 | 14 |
The marks in science of 80 students of class X are given below: Find the mode of the marks obtained by the students in science.
| Marks: | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| Frequency: | 3 | 5 | 16 | 12 | 13 | 20 | 5 | 4 | 1 | 1 |
Compute the mode of the following data:
| Class | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 |
| Frequency | 25 | 16 | 28 | 20 | 5 |
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.
Given below is the distribution of total household expenditure of 200 manual workers in a city:
| Expenditure (in Rs) | 1000 – 1500 | 1500 – 2000 | 2000 – 2500 | 2500 – 3000 | 3000 – 3500 | 3500 – 4000 | 4000 – 4500 | 4500 – 5000 |
| Number of manual workers |
24 | 40 | 31 | 28 | 32 | 23 | 17 | 5 |
Find the average expenditure done by maximum number of manual workers.
Compute the mode from the following data:
| Age (in years) | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 - 35 |
| No of patients | 6 | 11 | 18 | 24 | 17 | 13 | 5 |
One of the methods of determining mode is ______.
The relationship between mean, median and mode for a moderately skewed distribution is.
State the modal class.
| Class Interval | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 | 80 - 85 | 85 - 90 |
| Frequency | 5 | 20 | 10 | 10 | 9 | 6 | 12 | 8 |
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 |
Name the modal class.
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?
For the following distribution
| C.I. | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
| F | 20 | 30 | 24 | 40 | 18 |
the sum of lower limits of the modal class and the median class is?
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 ______.
For the following distribution
| Monthly Expenditure (Rs.) | No. of families |
| Expenditure less than Rs. 10,000 | 15 |
| Expenditure les than Rs. 13,000 | 31 |
| Expenditure les than Rs. 16,000 | 50 |
| Expenditure les than Rs. 19,000 | 67 |
| Expenditure les than Rs. 22,000 | 85 |
| Expenditure les than Rs. 25,000 | 100 |
The number of families having expenditure range (in ?) 16,000 - 19,000 is?
Mode is the value of the variable which has ______.
For the following distribution:
| Class | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 |
| Frequency | 10 | 15 | 12 | 20 | 9 |
The sum of lower limits of the median class and modal class is:
The weight of coffee in 70 packets are shown in the following table:
| Weight (in g) | Number of packets |
| 200 – 201 | 12 |
| 201 – 202 | 26 |
| 202 – 203 | 20 |
| 203 – 204 | 9 |
| 204 – 205 | 2 |
| 205 – 206 | 1 |
Determine the modal weight.
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 |
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 |
