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Edited By Sumit Saini | Updated on Jul 12, 2022 02:57 PM IST | #CBSE Class 10th

NCERT Solutions for Class 10 Maths exercise 14.4 - Cumulative frequency is calculated by adding all frequencies up to a certain threshold. We calculate the cumulative frequency by adding each and every frequency from the frequency distribution table given to us to the sum of its predecessor.

In NCERT solutions for Class 10 Maths chapter 14 exercise 14.4 we are introduced to ‘ogives’. An 'ogive of the less than type' is a graph of a cumulative frequency distribution of the less than type. An ‘ogive of the more than type' is a graph depicting a cumulative frequency distribution of the more than type. The median of the grouped frequency distribution is determined by the point of intersection of the ogives of more than and less than types.

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The formula for finding the median:

Where,

l = lower limit of median class,

n = number of observations,

cf = cumulative frequency of class preceding the median class,

f = frequency of median class,

h = class size (assuming class size to be equal).

Along with NCERT book Class 10 Maths chapter 14 exercise 14.4, the following exercises are also present.

** Q1 ** The following distribution gives the daily income of 50 workers of a factory.

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Daily Income (Upper-Class Limit) | Cumulative Frequency |

Less than 120 | 12 |

Less than 140 | 26 |

Less than 160 | 34 |

Less than 180 | 40 |

Less than 200 | 50 |

Now,

Taking upper-class interval on the x-axis and their respective frequencies on the y-axis,

** Q2 ** During the medical check-up of 35 students of a class, their weights were recorded as follows:

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Taking upper-class interval on the x-axis and their respective frequencies on the y-axis,

Marking a point on the curve whose ordinate is 17.5 gives an x-ordinate= 46.5.

Hence, the Median of the data is 46.5

Now,

Weight (Class) | Frequency | Cumulative Frequency |

>38 | 0 | 0 |

38-40 | 3 | 3 |

40-42 | 2 | 5 |

42-44 | 4 | 9 |

44-46 | 5 | 14 |

46-48 | 14 | 28 |

48-50 | 4 | 32 |

50-52 | 3 | 35 |

Median class = 46-48; Lower limit, l = 46;

Cumulative frequency of preceding class, c.f. = 14; f = 14; h = 2

Thus, the median using formula is 46.5 which verifies the result.

** Q3 ** The following table gives production yield per hectare of wheat of 100 farms of a village.

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

Production yield (Upper-Class Limit) | Cumulative Frequency |

More than or equal to 50 | 100 |

More than or equal to 55 | 98 |

More than or equal to 60 | 90 |

More than or equal to 65 | 78 |

More than or equal to 70 | 54 |

More than or equal to 75 | 16 |

Now,

Taking lower class limit on the x-axis and their respective frequencies on the y-axis,

The modal class is the class with the highest frequency in grouped data. The following formula can be used to determine the mode. When the modal class is unique, the formula is valid for equal class intervals.

The formula for finding the mode:

Where,

l = lower limit of modal class

h = class width

f1 = frequency of the modal class

f0 = frequency of the class preceding the modal class

f2 = frequency of the class succeeding the modal class

**Also Read| **** **Statistics Class 10 Notes

Exercise 14.4 Class 10 Maths, gives us a concept on STATISTICS and its uses to a board-level of graphs like ogives.

NCERT syllabus Class 10 Maths chapter 14 exercise 14.4 teaches us about the new formula of mode and median.

The concepts from Class 10 Maths chapter 14 exercise 14.4 will give us a vivid image of the graphical representation of Cumulative Frequency Distribution, which is very effective if ogives are given to us in any question.

**Also, See:**

As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

1. What is the main concept used to solve Class 10 Maths chapter 14 exercise 14.4?

To learn about graphical representation of cumulative frequency distribution. To find the median and mode using graphical method.

2. What do you understand by median?

The middle term of a sorted list is called as median. It may be the mean of the data set or close to the mean of the data set.

3. What do you understand by Cumulative Frequency Table for a set of data?

Cumulative frequency is a running total or the sum of the frequencies. This can be represented on a graph by plotting the upper boundary of the groups.

4. What do you understand by mode?

Any value that appears the most in the value set is called as the mode of the data set.

5. Write the formula for finding the mode of a set of data?

Any value that appears the most in the value set is called as the mode of the data set.

6. what is the relation between mean median and mode?

Generally

Mean – Mode = 3 (Mean – Median)

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6 minHave a question related to CBSE Class 10th ?

Hello

The Sadhu Ashram in Aligarh is located in Chhalesar . The ashram is open every day of the week, except for Thursdays . On Mondays, Wednesdays, and Saturdays, it's open from 8:00 a.m. to 7:30 p.m., while on Tuesdays and Fridays, it's open from 7:30 a.m. to 7:30 p.m. and 7:30 a.m. to 6:00 a.m., respectively . Sundays have varying hours from 7:00 a.m. to 8:30 p.m. . You can find it at Chhalesar, Aligarh - 202127 .

Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.

Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.

hello Zaid,

Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.

best of luck!

According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.

You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.

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