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Frequency polygon and frequency curve - class-XI

Description: frequency polygon and frequency curve
Number of Questions: 33
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Tags: statistics presentation of data economics data handling and analysis collection, organisation and presentation of data maths frequency distribution tables and graphs
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Fill in the blanks.

In 'Less Than" Ogive, the cumulative frequencies are written corresponding to the _______[P] limits of the classes of the given data.
In 'More Than' Ogive, the cumulative frequencies are written corresponding to the _
___[Q] limit of the classes.
On an ogive, point P whose y-coordinate $=n/2$ (i.e., half of the total number of the entries), has its x-coordinate equal to the _
____[R] of the data.
Two ogives, one 'less than' type and the other 'more than' type for the same data when drawn simultaneously on the same graph, intersect each other at the point P whose _
____[S] $=n/2$ and __________[T] $=$ median of the data where n is the total number of the entries of the data.

  1. P-Upper, Q-Lower, R-Median, S- y-coordinate, T-x-coordinate

  2. P-Lower, Q-Upper, R-Median, S-y-coordinate, T-x-coordinate

  3. P-Upper, Q-Lower, R-Median, S-x-coordinate, T-y-coordinate

  4. P-Upper, Q-Lower, R-Upper limit, S-y-coordinate, T-x-coordinate


Correct Option: A
Explanation:

In less than ogive, the curve is formed by joining upper limits of classes and cumulative frequencies as written corresponding to the upper limits of the given data.


In more than ogive, the curve is formed by joining lower limits of classes and cumulative frequencies as written corresponding to the lower limits of the given data.

$n/2$ on y-axis corresponds to the middle term of the observations when arranged in ascending order, giving us median of the data.

When both less than and more than Ogives are plotted on same graph, they both will intersect at the median as it remains the same for a given set of observations.
For x-coordinate giving Median, corresponding y-coordinate is $n/2$.

Hence, the answer is P-Upper, L-Lower, R-Median, S-y coordinate, T-x coordinate

Which one of the following  definitions is for frequency curve?

  1. The polygon formed by joining the middle points oft he tops of bars of the histogram.

  2. A special type of bar graph to represent a frequency distribution. Here the bars are drawn adjacent to each other, class intervals are represented on the horizontal axis and frequency on the vertical axis.

  3. If the class intervals are plotted on the horizontal axis and the cumulative frequencies on the vertical axis against the upper class boundaries then the free band curve through the points so plotted.

  4. The curve formed by joining the middle points of the tops of bars of the histogram.


Correct Option: D
Explanation:

Answer:- D) The curve formed by joining the middle points of the tops of bars of the histogram.

Reason:-
Frequency curve is defined as the curve formed by joining the middle points of the tops of the bars.

The measure of dispersion is a characteristics of :

  1. frequency polygon

  2. frequency curve

  3. frequency class

  4. frequency limit


Correct Option: B
Explanation:

There are following characteristics of $frequency curve$

$1$.Frequency curve identical in shape with different central locations.
$2.$frequency curve with same central location but different dispersion.
$3.$Frequency curve exist with different skewing.

Which one of the following is not a characteristics of frequency curve?

  1. measure of central tendency

  2. measure of dispersion

  3. frequency polygon

  4. shape of the frequency curve


Correct Option: C
Explanation:

Frequency polygon is not a characteristics of frequency curve.
Because frequency polygon is one kind of curve not a characteristics of frequency curve.

A frequency polygon is a graph that represents frequency distribution.

  1. True

  2. False


Correct Option: A

A curve obtained by plotting cumulative frequencies in called an Ogive.

  1. True

  2. False


Correct Option: A

A curve obtained by plotting cumulative frequencies is called an Ogive.

  1. True

  2. False


Correct Option: A

Ogive curve can be drawn for __________.

  1. more than type distribution

  2. less than type distribution

  3. both (a) and (b)

  4. none of (a) and (b)


Correct Option: C

With the help of ogive curve, one can determine __________.

  1. median

  2. quartile

  3. percentiles

  4. all the above


Correct Option: D

Ogives for more than type and less than type distributions intersect at ________.

  1. mean

  2. median

  3. mode

  4. none of them


Correct Option: B

If we plot the points of a less than type or more than type frequency distribution, the shape of graph is _________.

  1. ogive curve

  2. scatter diagram

  3. zig-zag curve

  4. parabola


Correct Option: A

Non-dimensional diagrams are also known as __________.

  1. cubes

  2. spheres

  3. pictograms

  4. all the above


Correct Option: C

Choice of a particular chart depends on ________.

  1. the purpose of study

  2. the type of data

  3. the nature of data

  4. all the above


Correct Option: D

It is necessary to find cumulative frequencies in order to draw a/an __________.

  1. pie chart

  2. frequency polygon

  3. ogive curve

  4. column chart


Correct Option: C

In an Ogive curve, the points are plotted for __________.

  1. the values and frequencies

  2. frequencies and cumulative frequencies

  3. None of the above

  4. Both a and b


Correct Option: C

The graph of successive points of a distribution joined by straight lines in statistical terminology is known as _________.

  1. frequency polygon

  2. frequency curve

  3. trend

  4. cumulative distribution curve


Correct Option: A

Draw frequency polygon and frequency curve for the following data on land holding by the farmers.

Area in hectare 11 - 20 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80
No. of farmers 58 103 208 392 112 34 12
  1. Area in hectaresClass markNo. of farmers

    1 -105.50

    11 -2015.558

    21 -3025.5103

    31 -4035.5208

    41 -5045.5392

    51 -6055.5112

    61 -7065.534

    71 -8075.512

    81 -9085.50

  2. Area in hectaresClass markNo. of farmers

    1 -105.50

    11 -2015.558

    21 -3025.5103

    31 -4035.5208

    41 -5045.5392

    51 -6055.5112

    61 -7065.535

    71 -8075.512

    81 -9085.50

  3. Area in hectaresClass markNo. of farmers

    1 -105.50

    11 -2015.558

    21 -3025.5103

    31 -4035.5208

    41 -5045.5392

    51 -6055.5112

    61 -7065.534

    71 -8075.515

    81 -9085.50

  4. Area in hectaresClass markNo. of farmers

    1 -105.50

    11 -2015.558

    21 -3025.5106

    31 -4035.5208

    41 -5045.5392

    51 -6055.5112

    61 -7065.534

    71 -8075.512

    81 -9085.50


Correct Option: A
Explanation:

Solution:

Area in hectares Class mark No. of farmers
1  -10 5.5 0
11 -20 15.5 58
21 -30 25.5 103
31 -40 35.5 208
41 -50 45.5 392
51 -60 55.5 112
61 -70 65.5 34
71 -80 75.5 12
81 -90 85.5 0
Class Interval Cumulative Frequency
10-19 8
20-29 19
30-39 23
40-49 30

Construct a frequency distribution table from the following cumulative frequency distribution $:$

  1.  8
     19
     23
     30

     

  2.  30
     23
     19
     8

     

  3.  8
     27
     50
     80

     

  4.  8
     11
     4
     7

     


Correct Option: D
Explanation:

$\Rightarrow$  The frequency distribution table are as follows :

$Class\,Interval$ $Cumulative\,Frequency$  $Frequency$ 
$10-19$  $8$  $8$ 
$20-29$  $19$  $19-8=11$ 
$30-39$  $23$  $23-19=4$ 
$40-49$  $30$  $30-23=7$ 

How a frequency curve is sketched?

  1. Frequency curve is sketched with the help of histogram by joining the end points of rectangles.

  2. Frequency curve is sketched with the help of histogram by joining the mid point of rectangle.

  3. Frequency curve is sketched with the help of histogram by joining the starting points of rectangles. 

  4. None of these


Correct Option: B
Explanation:

Curve formed by joining the midpoint of rectangular of histogram is called as frequency curve.

To show the trend for a variable, which one of the presentation method is used?

  1. Histogram

  2. Frequency polygon

  3. Line graph

  4. Scatter graph


Correct Option: C

Fill the Alternative given in the bracket:
_______ is a graph of cumulative frequency distribution.

  1. Histogram

  2. Frequency Polygon

  3. Ogives

  4. Pie-diagram


Correct Option: C

Fill the Alternative given in the bracket:
_______ is a graph representing a frequency distribution.

  1. Frequency polygon

  2. Histogram

  3. Pie diagram

  4. Bar diagram


Correct Option: A

Fill the alternative given in the bracket:
Vertical rectangle representing class frequency in a frequency distribution is called _________.

  1. bar diagram

  2. histogram

  3. pie diagram

  4. frequency polygon


Correct Option: B

Fill the Alternative given in the bracket:
A frequency polygon is a ________ curve.

  1. freehand

  2. joint

  3. straight line

  4. multi dimensional


Correct Option: C

From the below mentioned what, if missed, makes the graphic presentation incomplete

  1. Unit of measurement

  2. Suitable scale

  3. Suitable title

  4. All of the above


Correct Option: D

Graph is a useful tool as _______________.

  1. only limited information can be achieved

  2. information provided is not useful for an expert

  3. not precisely correct

  4. it does not require that the person who is using graph should know mathematics


Correct Option: D

For drawing a frequency polygon of a continous frequency distribution, we plot the points whose ordinates are the frequencies of the respective classes and abcissae are respectively :

  1. upper limits of the classes

  2. lower limits of the classes

  3. class marks of the classes

  4. upper limits of perceeding classes


Correct Option: C
Explanation:

We draw the class marks on the abscissae, class marks are the mean of lower and upper limit of the class intervals.

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