Advertisements
Advertisements
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 |
उत्तर
The given data is shown below.
| Monthly Consumption (in units) | No. of consumers (fi) | xi | fixi | C.f. |
| 65−85 | 4 | 75 | 300 | 4 |
| 85−105 | 5 | 95 | 475 | 9 |
| 105−125 | 13 | 115 | 1495 | 22 |
| 125−145 | 20 | 135 | 2700 | 42 |
| 145−165 | 14 | 155 | 2170 | 56 |
| 165−185 | 8 | 175 | 1400 | 64 |
| 185−205 | 4 | 195 | 780 | 68 |
| Total | `sumf=68` | `sumf_1x_1=9320` |
Here, the maximum frequency is 20 so the modal class is 125 − 145.
Therefore,
l = 125, h = 20, f = 20, f1 = 13 and f2 = 14
Mode `=l+(f-f_1)/(2f-f_1-f_2)xxh`
`=125+7/13xx20`
`=125+140/13`
= 125 + 10.76
= 135.76
Mode = 135.76 units
Thus, the mode of the monthly consumption of electricity is 135.76 units.
Mean `=(sumf_1x_1)/(sumf)`
`=9320/68=137.05`
Mean = 137.05
Thus, the mean of the monthly consumption of electricity is 137.05 units.
Here,
Total number of consumers, N = 68 (even)
Then, `N/2=34`
Median `=l+(N/2_f)/fxxh`
`=125+(68/2_22)/20xx20`
`=125+(34-22)/20xx20`
`=125+12/20xx20`
= 125 + 12
= 137
Thus, the median of the monthly consumption of electricity is 137 units.
संबंधित प्रश्न
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 |
| Frequency | 10 | 35 | 52 | 61 | 38 | 29 |
Determine the modal lifetimes of the components.
The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.
| Number of students per teacher |
Number of states/U.T. |
| 15 − 20 | 3 |
| 20 − 25 | 8 |
| 25 − 30 | 9 |
| 30 − 35 | 10 |
| 35 − 40 | 3 |
| 40 − 45 | 0 |
| 45 − 50 | 0 |
| 50 − 55 | 2 |
Compare the modal ages of two groups of students appearing for an entrance test:
| Age (in years): | 16-18 | 18-20 | 20-22 | 22-24 | 24-26 |
| Group A: | 50 | 78 | 46 | 28 | 23 |
| Group B: | 54 | 89 | 40 | 25 | 17 |
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 series:
| Size | 45 – 55 | 55 – 65 | 65 – 75 | 75 – 85 | 85 – 95 | 95 – 105 | 105 - 115 |
| Frequency | 7 | 12 | 17 | 30 | 32 | 6 | 10 |
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 |
Mode is
The following frequency table shows the demand for a sweet and the number of customers. Find the mode of demand of sweet.
|
Weight of sweet (gram)
|
0 - 250 | 250 - 500 | 500 - 750 | 750 - 1000 | 1000 - 1250 |
| No. of customers | 10 | 60 | 25 | 20 | 15 |
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 |
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 |
What is the frequency of the class preceding the modal class?
Find the mode of the given data: 3.1, 3.2, 3.3, 2.1, 1.3, 3.3, 3.1
Find the mode of the following data:
| Marks | 0 − 10 | 10 − 20 | 20 − 30 | 30 − 40 | 40 − 50 |
| Number of students | 22 | 38 | 46 | 34 | 20 |
Find the mode of the following distribution:
| Weight (in kgs) | 25 − 34 | 35 − 44 | 45 − 54 | 55 − 64 | 65 − 74 | 75 − 84 |
| Number of students | 4 | 8 | 10 | 14 | 8 | 6 |
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?
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 |
Which of the following is not a measure of central tendency?
If mode of the following frequency distribution is 55, then find the value of x.
| Class | 0 – 15 | 15 – 30 | 30 – 45 | 45 – 60 | 60 – 75 | 75 – 90 |
| Frequency | 10 | 7 | x | 15 | 10 | 12 |
