# Cumulative Frequency Distribution of Less Than Type

## Trending Questions

**Q.**

How to find missing frequency in median

For example:

If the median of the distribution given below is 46, find the value of the missing frequencies.

class interval | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |

Frequency | 12 | 30 | f1 | 65 | f2 | 25 | 18 |

**Q.**Question 7

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

Weight (in kg)40−4545−5050−5555−6060−6565−7070−75Number of students 2386632

**Q.**

The following table gives the life-time (in days) of 100 electric bulbs of a certain brand.

Life−time(in days)Less than 50Less than 100Less than 150Less than 200Less than 250Less than 300Number of bulbs721527991100

From this table, construct the frequency distribution table.

**Q.**

Which of the given less than cumulative frequency curve (ogive) correctly represents the following distribution?

Height110−120120−130130−140140−150150−160Number of students 7 9 12 10 4

**Q.**Find the value of p for the following distribution whose mean is 16.6.

x: | 8 | 12 | 15 | p | 20 | 25 | 30 |

f: | 12 | 16 | 20 | 24 | 16 | 8 | 4 |

**Q.**

The following table shows the distribution of the daily wages earned by workers in a building site.

Wages (in Rs/day) | $50-60$ | $60-70$ | $70-80$ | $80-90$ | $90-100$ | $100-110$ | $110-120$ | $120-130$ |

No. of workers | $12$ | $20$ | $30$ | $38$ | $24$ | $16$ | $12$ | $8$ |

Change the distribution to a more than type distribution and draw its ogive. Hence, obtain the median wage per day from the graph.

**Q.**

The following table shows the distribution of the heights of a group of factory workers :

Ht. (cm):150−155155−160160−165165−170170−175175−180180−185No. of workers61218201386

(i) Determine the cumulative frequencies.

(ii) Draw the 'less than' cumulative frequency curve on graph paper. Use 2 cm = 5 cm height on one axis and 2 cm = 10workers on the other.

**Q.**

The frequency distribution table below shows the marks of students. Find the number of people who obtained marks less than 22.5.

Class12.5−17.517.5−22.522.5−27.527.5−32.532.5−37.5Frequency222191413

21

22

23

24

**Q.**

(a) Use the information given in the adjoining histogram to construct a frequency table.

(b) Use this table to construct an ogive

**Q.**

The following table gives production yield per hectare of wheat of 100 farms of a village.

Production yield (in kg/ha) |
50 − 55 |
55 − 60 |
60 − 65 |
65 − 70 |
70 − 75 |
75 − 80 |

Number of farms |
2 |
8 |
12 |
24 |
38 |
16 |

Change the distribution to a more than type distribution and draw ogive.

**Q.**

Which of the following are the possible ages of 27th and 32nd observations in the given grouped distribution in increasing order of age? All the persons (observations) part of the distribution have exact integral ages.

Age less thanNumber of people15316111721183119362040

- 15, 16
- 17, 18
- 18, 19
- 14, 15

**Q.**Question 7

Consider the following frequency distribution

Class0.56−1112−1718−2324−29Frequency131015811

The upper limit of the median class is

(a) 17

(b) 17.5

(c) 18

(d) 18.5

**Q.**

Question 5

The following table gives the distribution of the life time of 400 neon lamps:

Life time (in hours)Number of lamps1500−2000142000−2500562500−3000603000−3500863500−4000744000−4500624500−500048

Find the median life time of a lamp.

**Q.**Draw a less than ogive for the following frequency distribution

Marks | No. of students |

0 - 4 | 8 |

4 - 8 | 4 |

8 - 12 | 6 |

12 - 16 | 12 |

16 - 20 | 10 |

- (4, 6) (6 , 10) (12, 22) (18, 28) (20, 32)
- (4, 10) (8, 10) (12, 20) (18, 28) (20, 32)
- (4, 8) (8, 12) (12, 18) (16, 30) (20, 40)
- (6, 4) (8, 10) (12, 20) (18, 26) (22, 32)

**Q.**

Find the Median for the given data by drawing a 'less than ogive' :

Class Interval0−1010−2020−3030−4040−50Frequency51014168

35

28

29

31

**Q.**

Find the median for the following data

Class interval0−1010−2020−3030−4040−5050−60Frequency162032483014

**Q.**The following table gives the production yield per hectare of wheat of 100 farms of a village.

Production yield in kg/hectare | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 | 75-80 |

Number of frames | 2 | 8 | 12 | 24 | 38 | 16 |

Change the above distribution to more than type distribution and draw its ogive.

**Q.**The table below gives the volume of water (in litres) Suzanne drank in the last 40 days. Find the median of this data.

Volume Numberof water(l) of days1−262−383−4124−565−68

- 2
- 4
- 3.5
- 5.5

**Q.**Draw a histogram and frequency polygon for the following frequency distribution.

Class | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 |

Frequency | 20 | 30 | 50 | 40 | 10 |

**Q.**

Find the median of the following data.

Class interval0−1010−2020−3030−4040−50Frequency81014108

**Q.**Find the missing value of p for the following distribution whose mean is 12.58

x: | 5 | 8 | 10 | 12 | p | 20 | 25 |

f: | 2 | 5 | 8 | 22 | 7 | 4 | 2 |

**Q.**

In a survey of 200 students from 7 different schools, 50 people do not play only NFS, 40 people do not play only Dota and 10 people play no online games. Then find the no. of people out of 200 people who do not play both the games.

{3}

{1, 2, 3, 4}

{1, 2, 4, 5}

{1, 2, 3, 4, 5, 6}

**Q.**

The monthly income of a group of 320 employees in a company is as follows :

Monthly income (in Rs.1000) 6 – 7 7 – 8 8 – 9 9 – 10 10 – 11 11 – 12 12 – 13

Number of employees 20 45 65 95 60 30 5

Draw an ogive for the given distribution taking 2cm = Rs.1000 on one axis & 2cm = 50 employees on the other axis. Using the graph determine:

930, 20, 25000

800, 20, 20000

930, 10, 15000

930, 15, 10250

800, 10, 20000

800, 15, 10250

800, 20, 15100

**Q.**Following is the distribution of marks of 70 students in a periodical test:

Marks | Number of students |

Marks less than 10 Marks less than 20 Marks less than 30 Marks less than 40 Marks less than 50 |
3 11 28 48 70 |

Draw a cumulative frequency curve for the above data and find the median.

**Q.**

Weekly wages(in Rs.)0−100100−200200−300300−400400−500Number of workers4039343045

What is the number of people whose wage is less than Rs.400?

40

79

139

143

**Q.**Which measure of central tendency is obtained graphically as the x coordinate of the point of intersection of the two ogives?

(a) Mean

(b) Median

(c) Mode

(d) None of these

**Q.**

Find the median of the following cumulative frequency distribution:

xfrequencyCumulative frequency221134233925458135482156930684347843884240

49.5

53.5

54

55

**Q.**The median of a given frequency distribution is found graphically with the help of __________.

- Frequency polygon
- Histogram
- Frequency curve
- Ogive

**Q.**From the frequency distribution of student marks, find the number of students who scored less than 22.5 marks. Class12.5−17.517.5−22.522.5−27.527.5−32.532.5−37.5Frequency222191413

- 21
- 22
- 23
- 24

**Q.**Draw an Ogive for the following frequency distribution by less than method and also find its median from the graph

Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

Number of students | 7 | 10 | 23 | 51 | 6 | 3 |