Graphical Representation of Cumulative Frequency Distribution

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Statistics and Probability
Statistics
- Concepts of Statistics
- Mean of Grouped Data
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- Graphical Representation of Cumulative Frequency Distribution
- Concepts of Statistics
- Ogives (Cumulative Frequency Graphs)
Probability
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Internal Assessment

Notes

In this concept we will study about Relation of Ogive and Median. These graphical representation of the frequency distribution are called Ogives. Actual limits are on the x-axis and cumulative frequencies on the y-axis.

Ogive is also known as cumulative frequency distribution.

You will be asked to draw either a less than frequency ogive or more than frequency ogive.

Example: The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution :

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

1) Less than type cumulative frequency table

Classes	cf
Less than 10	2
Less than 15	14
Less than 20	16
Less than 25	20
Less than 30	23
Less than 35	27
Less than 40	30

2) More than type cumulative frequency table

Classes	cf
More than 5	30
More than 10	28
More than 15	16
More than 20	14
More than 25	10
More than 30	7
More than 35	3

The graphical representation of both the ogives will be

Here, $\frac{N}{2} = \frac{30}{2} = 15$

Now, we will take 15 on y axis and draw a perpendicular line that touches the curve, and from the point where the perpendicular touches the curve draw a perpendicular that touches the x axis, the point at which the perpendicular touches the x axis is the median.

Thus, here the Median is 17.5

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Related QuestionsVIEW ALL [54]

The following is the distribution of weights (in kg) of 40 persons:

Weight (in kg)	40 – 45	45 – 50	50 – 55	55 – 60	60 – 65	65 – 70	70 – 75	75 – 80
Number of persons	4	4	13	5	6	5	2	1

Construct a cumulative frequency distribution (of the less than type) table for the data above.

Calculate the missing frequency form the following distribution, it being given that the median of the distribution is 24

Age (in years)	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Number of persons	5	25	?	18	7

The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution:

Monthly Consumption (in units)	140 – 160	160 – 180	180 – 200	200 – 220	220 – 240	240 – 260	260 - 280
Number of Families	3	8	15	40	50	30	10

Prepare a ‘more than type’ ogive for the given frequency distribution.

For a frequency distribution, mean, median and mode are connected by the relation

In the formula $\bar{x} = a + h (\frac{\sum f_{i} u_{i}}{\sum f_{i}})$ , for finding the mean of grouped frequency distribution u_i = ______.

Change the following distribution to a 'more than type' distribution. Hence draw the 'more than type' ogive for this distribution.

Class interval:	20−30	30−40	40−50	50−60	60−70	70−80	80−90
Frequency:	10	8	12	24	6	25	15

If $u_{i} = \frac{x_{i} - 25}{10}, Σ f_{i} u_{i} = 20, Σ f_{i} = 100, then$ $\bar{X}$

If the median of the following frequency distribution is 32.5. Find the values of f₁ and f_2.

Graphical Representation of Cumulative Frequency Distribution

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Topics

Number Systems

Real Numbers

Algebra

Polynomials

Pair of Linear Equations in Two Variables

Quadratic Equations

Arithmetic Progressions

Coordinate Geometry

Lines (In Two-dimensions)

Constructions

Geometry

Triangles

Circles

Trigonometry

Introduction to Trigonometry

Trigonometric Identities

Some Applications of Trigonometry

Mensuration

Areas Related to Circles

Surface Areas and Volumes

Statistics and Probability

Statistics

Probability

Internal Assessment

Notes

Related QuestionsVIEW ALL [54]

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