Consider the following frequency distribution:
| Class | 1 – 5 | 6 – 10 | 11 – 15 | 16 – 20 | 21 – 25 |
|---|---|---|---|---|---|
| Frequency | 13 | 10 | 15 | 8 | 11 |
The upper limit of the median class is
Consider the data :
| Class | Frequency |
|---|---|
| 65-85 | 4 |
| 85-105 | 5 |
| 105-125 | 13 |
| 125-145 | 20 |
| 145-165 | 14 |
| 165-185 | 7 |
| 185-205 | 4 |
The difference of the upper limit of the median class and the lower limit of the modal class is
For the following distribution:
| Marks | Number of students |
|---|---|
| Below 10 | 3 |
| Below 20 | 12 |
| Below 30 | 27 |
| Below 40 | 57 |
| Below 50 | 75 |
| Below 60 | 80 |
The modal class is
The weight of coffee in 70 packets are shown in the following table:
| Weight (in g) | Number of packets |
|---|---|
| 200-201 | f |
| 201-202 | 26 |
| 202-203 | 20 |
| 203-204 | 9 |
| 204-205 | 2 |
| 205-206 | 1 |
If the modal weight is 201.7 kg then find the missing frequency.
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 |
What is the modal class of given data?
The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below :
| Mileage (km/l) | Number of cars |
|---|---|
| 10-12 | 7 |
| 12-14 | 12 |
| 14-16 | 18 |
| 16-18 | 13 |
Find the mean mileage.
The daily income of a sample of 50 employees are tabulated as follows:
| Income (in Rs) | Number of employees |
|---|---|
| 1-200 | 14 |
| 201-400 | 15 |
| 401-600 | 14 |
| 601-800 | 7 |
Find the mean daily income of employees by the assumed mean method.
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.
Find the mean of the distribution :
| Class | Frequency |
|---|---|
| 1-3 | 9 |
| 3-5 | 22 |
| 5-7 | 27 |
| 7-10 | 17 |
The following table gives the number of pages written by Sarika for completing her own book for 30 days :
| Number of pages written per day | Number of days |
|---|---|
| 16-18 | 1 |
| 19-21 | 3 |
| 22-24 | 4 |
| 25-27 | 9 |
| 28-30 | 13 |
Find the mean number of pages written per day.
Calculate the mean of the scores of 20 students in a mathematics test :
| Marks | Number of students |
|---|---|
| 10-20 | 2 |
| 20-30 | 4 |
| 30-40 | 7 |
| 40-50 | 6 |
| 50-60 | 1 |
Weekly income of 600 families is tabulated below :
| Weekly income | Number of families |
|---|---|
| 0-1000 | 250 |
| 1000-2000 | 190 |
| 2000-3000 | 100 |
| 3000-4000 | 40 |
| 4000-5000 | 15 |
| 5000-6000 | 5 |
| **TOTAL** | **600** |
Compute the median income.
Calculate the mean of the following data by the direct method.
| Class | Frequency |
|---|---|
| 4 – 7 | 5 |
| 8 –11 | 4 |
| 12– 15 | 9 |
| 16 –19 | 10 |
The mean of the below data is 35. Find the missing frequency using the direct method.
| Marks | Number of students |
|---|---|
| 10-20 | 2 |
| 20-30 | f |
| 30-40 | 7 |
| 40-50 | 6 |
| 50-60 | 1 |
An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table :
| Number of seats | Frequency |
|---|---|
| 100-104 | 15 |
| 104-108 | 20 |
| 108-112 | 32 |
| 112-116 | 18 |
| 116-120 | 15 |
Determine the mean number of seats occupied over the flights by the assumed mean method.
The monthly income of 100 families are given as below :
| Income (in Rs) | Number of families |
|---|---|
| 0-5000 | 8 |
| 5000-10000 | 26 |
| 10000-15000 | 41 |
| 15000-20000 | 16 |
| 20000-25000 | 3 |
| 25000-30000 | 3 |
| 30000-35000 | 2 |
| 35000-40000 | 1 |
Calculate the modal income.
The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follows:
| Speed (km/h) | Number of players |
|---|---|
| 85-100 | 11 |
| 100-115 | 9 |
| 115-130 | 8 |
| 130-145 | 5 |
Calculate the median bowling speed.
The weights (in kg) of 50 wrestlers are recorded in the following table:
| Weight (in kg) | Number of wrestlers |
|---|---|
| 100-110 | 4 |
| 110-120 | 14 |
| 120-130 | 21 |
| 130-140 | 8 |
| 140-150 | 3 |
Find the mean weight of the wrestlers by the assumed mean method.
Find the mean marks of the students for the following distribution:
| Marks | Number of Students |
|---|---|
| 0 and above | 80 |
| 10 and above | 77 |
| 20 and above | 72 |
| 30 and above | 65 |
| 40 and above | 55 |
| 50 and above | 43 |
| 60 and above | 28 |
| 70 and above | 16 |
| 80 and above | 10 |
| 90 and above | 8 |
| 100 and above | 0 |
The median of the following data is 50. Find the values of p and q, if sum of all the frequencies is 90.
| Marks | _f_ |
|---|---|
| 20–30 | p |
| 30–40 | 15 |
| 40–50 | 25 |
| 50–60 | 20 |
| 60–70 | q |
| 70–80 | 8 |
| 80–90 | 10 |
Find the mean age of 100 residents of a town from the following data by using the step-deviation method.
| Age | Number of persons |
|---|---|
| equal and above 0 | 100 |
| equal and above 10 | 90 |
| equal and above 20 | 75 |
| equal and above 30 | 50 |
| equal and above 40 | 25 |
| equal and above 50 | 15 |
| equal and above 60 | 5 |
| equal and above 70 | 0 |
The mean of following frequency distribution is 50, but the frequencies f1 and f2 in classes (20–40) and (60–80) respectively are not known. Find these frequencies, if the sum of all the frequencies is 120.
| Class | Frequency |
|---|---|
| 0–20 | 17 |
| 20–40 | f<sub>1</sub> |
| 40–60 | 32 |
| 60–80 | f<sub>2</sub> |
| 80–100 | 19 |
Determine the mean of the following distribution:
| Marks | Number of Students |
|---|---|
| Below 10 | 5 |
| Below 20 | 9 |
| Below 30 | 17 |
| Below 40 | 29 |
| Below 50 | 45 |
| Below 60 | 60 |
| Below 70 | 70 |
| Below 80 | 78 |
| Below 90 | 83 |
| Below 100 | 85 |
The weight of tea in 70 packets are shown in the following table:
| Weight (in g) | Number of packets |
|---|---|
| 200–201 | 13 |
| 201–202 | 27 |
| 202–203 | 18 |
| 203–204 | 10 |
| 204–205 | 1 |
| 205–206 | 1 |
Find the mean weight of packets.