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Histograms - class-VI

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________ is a set of rectangles with bases as the intervals between class 
boundaries (along X-axis) and with are as proportional to the class frequency.

  1. Bar diagram

  2. Component bar diagram

  3. Histogram

  4. Multiple bar diagram


Correct Option: C

Histogram is a type of _____.

  1. Geometric diagram

  2. Frequency diagram

  3. Both A and B

  4. Arithmetic line graph


Correct Option: B

Which of the following are differences between bar diagram and histogram?

  1. In a histogram, no space is left in between two rectangles, but in a bar diagram some space must be left between consecutive bars

  2. The width of a bar is unimportant for the purpose of comparison. The width in a histogram is as important as its height.

  3. We can have a bar diagram both for discrete and continuous variables, but the histogram is drawn only for a continuous variable.

  4. All of these


Correct Option: D

Histogram is suitable for the data presented as _________.

  1. continuous grouped frequency distribution

  2. discrete grouped frequency distribution

  3. individual series

  4. all the above


Correct Option: A

Histogram also gives value of _______ of the frequency distribution graphically

  1. mode

  2. mean

  3. median

  4. all of these


Correct Option: A

Histogram give a graphical presentation of a continuous frequency distribution.

  1. True

  2. False


Correct Option: A

Histogram give a graphical presentation of a continuous frequents distribution.

  1. True

  2. False


Correct Option: A

When in a frequency distribution class widths are not same we have to draw histogram then,

  1. We mark class size as width and the given frequency as length and draw the rectangle

  2. We reduce class size to minimum class size keeping the length same

  3. We find the proportionate lengths of the class corresponding to minimum width and draw the rectangle.

  4. None of these


Correct Option: C
Explanation:

When in a frequency distribution class widths are not same we have to draw histogram then,We find the proportionate lengths of the class corresponding to minimum width and draw the rectangle.
Answer (C) 
We find the proportionate lengths of the class corresponding to minimum width and draw the rectangle.

With the help of histogram we can prepare _________.

  1. frequency polygon

  2. frequency curve

  3. frequency distribution

  4. all of the above


Correct Option: D

Histogram is suitable for ________.

  1. time series data

  2. chronological distribution

  3. none of (a) or (b)

  4. both (a) and (b)


Correct Option: D

In a histogram with equal class intervals; heights of bar are proportional to _________.

  1. mid-vales of the class

  2. frequencies of respective classes

  3. either (a) or (b)

  4. neither (a) nor (b)


Correct Option: B

Classification is applicable in case of  ______.

  1. quantitative data

  2. qualitative data

  3. both (a) and (b)

  4. none of the above


Correct Option: C

Which of the statement is correct?

  1. Histograms and historigrams are similar in look

  2. Cube and square diagrams are similar in look

  3. Pie-chart and ogives are similar in look

  4. None of them


Correct Option: A

The following frequency distribution is classified as 

Classes Frequency
0-50 25
0-30 18
0-10 5
  1. cumulative distribution in less than type

  2. Cumulative distribution in more than type

  3. discrete frequency distribution

  4. cumulative frequency distribution


Correct Option: A

A core distribution data is given for an inventory measuring physical fitness. The type of graph that will be used to display the information will be _______________.

  1. Histogram

  2. Line graph

  3. Pie chart

  4. Bar graph


Correct Option: A

The most common form of diagrammatic representation of a grouped frequency distribution is -

  1. Ogive

  2. Histogram

  3. Frequency polygon

  4. None of these


Correct Option: B
Explanation:

Answer:- B) Histogram

Reason:-
Histogram is easy to use and we can plot the curve, also we can find the areas of adjoining rectangles which is proportional to class frequencies.

When rectangles are drawn with the areas proportional to the frequencies of respective class intervals, what is the diagram called? 

  1. Bar graph

  2. Frequency polygon

  3. Pie graph

  4. Histogram


Correct Option: D
Explanation:

The histograms are diagrams which represent the class interval and the frequency in the form of a rectangle. 

There will be as many adjoining rectangles as there are class intervals. 
So, when rectangles are drawn with the areas proportional to the frequencies of respective class intervals, the diagram called Histogram.
Therefore, option D is correct.

In histogram, the height of rectangle shows _____

  1. width of the class

  2. upper limit of the class

  3. lower limit of the class

  4. frequency of the class


Correct Option: D
Explanation:

histogram is a display of statistical information that uses rectangles to show the frequency of data items in successive numerical intervals of equal size.

Hence, height of the rectangle represents the frequency of the class.

Histogram are a great way to show results of 

  1. categories

  2. continuous data

  3. both $A$ and $B$

  4. None of these


Correct Option: B
Explanation:

Answer:-

B) Continuous data
Histogram is curve that is represented in the form of bars for continuous data.

Which type of data can be represented by histogram?

  1. Grouped data

  2. Ungrouped data

  3. Continuous data

  4. None of these


Correct Option: A
Explanation:

Histogram represents grouped data 

Data on percentage distribution of area of land in acres owned by households in two districts of a particular state as follows:

Land holding District-A District-B
$0.01-0.99$ $5.62$ $13.53$
$1.0-2.49$ $18.35$ $21.84$
$2.5-7.49$ $47.12$ $39.32$
$7.5-12.49$ $19.34$ $12.15$
$12.5-19.99$ $7.21$ $7.43$
$20.0-29.99$ $2.36$ $5.73$

What is the appropriate diagram to represent the above data?

  1. Pie diagram

  2. Histogram

  3. Bar chart

  4. NONE OF THE ABOVE


Correct Option: B
Explanation:

Appropriate diagram to represent given data is histogram because histogram easily represents graph of 2 different district on the same graph & in easy to understand graph

Which one of the following statements is not correct with reference to a histogram?

  1. Frequency curve is obtained by joining the midpoints of the top of the adjacent rectangles with smooth curves

  2. Histogram is drawn for continuous data

  3. The height of the bar is proportional to the frequency of that class

  4. Mode of the distribution can be obtained from the histogram


Correct Option: C
Explanation:

Option C is not correct & all other are correct from our basic knowledge of statistics

Histograms, pie charts and frequency polygons are all types of

  1. one dimension diagrams

  2. two dimension diagrams

  3. cumulative diagrams

  4. none of these


Correct Option: A
Explanation:

Using these we can vary one component only

Types of histograms includes

  1. deviation bar charts

  2. paired bar charts

  3. grouped charts

  4. all of the above


Correct Option: D
Explanation:

All are the types of histogram

Histograms is classified as one dimensional diagrams because only

  1. length is considered

  2. width is considered

  3. length plus width is considered

  4. none of these


Correct Option: A
Explanation:

$\Rightarrow$  Histogram is classified as one dimensional diagrams because only $Legth\,is\,considered.$

$\Rightarrow$  A histogram is a display of statistical information that uses rectangles to show the frequency of data items in successive numerical intervals of equal size. 
$\Rightarrow$  In the most common form of histogram, the independent variable is plotted along the horizontal axis and the dependent variable is plotted along the vertical axis.
$\Rightarrow$  The data appears as colored or shaded rectangles of variable area.

Sum of all components in normalized histogram is equal to

  1. $0$

  2. $2$

  3. $100$

  4. $1$


Correct Option: D
Explanation:

$\Rightarrow$  Sum of all components in normalized histogram is equal to $1$

$\Rightarrow$  The histogram of a digital image with intensity levels in the range $[0,L-1]$ is a discrete function, $h(r _k)=n _k$, where, $r _k$ is $k^{th}$ intensity value and $n _k$ is the number of pixels in the image with intensity, $r _k$.
$\Rightarrow$  It is a common practice to normalize a histogram by dividing each of its components by total number of pixels in the image, denoted by a matrix $M\times N$, where $M$ and $N$ are the row and column dimension of the image. Thus a normalized histogram is given by the following equation,

$P(r _k)=\dfrac{n _k}{M\times N}for\,k=0,1...L-1$

Probability density functions are always

  1. decreasing

  2. increasing

  3. positive

  4. negative


Correct Option: C
Explanation:

Probablity of a function is always greater than 0 i.e. positive

PDF in histogram equalization stands for

  1. probability dual function

  2. partial density function

  3. parametric density function

  4. probability density function


Correct Option: D
Explanation:

PDF in histogram equalization stands for probability density function. 

Local histogram processing deals with

  1. whole image

  2. slices of image

  3. centre of image

  4. none of these


Correct Option: B
Explanation:

In local histogram we deal with slice of images

Strictly monotonical function guarantee inverse mapping as

  1. single valued

  2. multi valued

  3. dual valued

  4. none of these


Correct Option: A

Histogram is technique processed in

  1. intensity domain

  2. frequency domain

  3. spatial domain

  4. none of these


Correct Option: C
Explanation:

Well known from application of histogram

The statistical data can be represented by diagram using 

  1. Histogram

  2. Frequency polygon

  3. Ogive

  4. None of these


Correct Option: A,B,C
Explanation:

It is fundamental concept that a statistical data can be represented using plotting graph between different variable, pie chart, histogram, frequency polygon or frequency table or ogives.
Hence, $A,B,C$ are correct choices.

In a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement.
If true then enter $1$ and if false then enter $0$

  1. $1$

  2. $0$

  3. can't determine

  4. None of these


Correct Option: B
Explanation:

No, this is not a correct statement.
In a histogram, horizontal axis represents the class intervals whose width is fixed & the varying data is plotted along the y-axis. So in all  the rectangles of a histogram, width remains same & the length changes.
So correct statement is "In a histogram, the area of each rectangle is proportional to the frequency of its class."

The width of a rectangle in a histogram represents ___________ of the class.

  1. frequency

  2. range

  3. class limit

  4. upper limit


Correct Option: A
Explanation:

The height of the rectangle in the histogram represents the frequency.

For which of these would you use a histogram to show the data?
$(a)$ The number of letters for different areas in a postman's bag.
$(b)$ The height of competitors in an athletics meet.
$(c)$ The number of cassettes produced by $5$ companies.
$(d)$ The number of passengers boarding trains from $7{:}00$ a.m. to $7{:}00$ p.m. at a station.
Give reasons for each.

  1. $a$

  2. $b$

  3. $c$

  4. $d$


Correct Option: B,D
Explanation:

Histograms are a special form of bar chart where the data represents continuously rather than discrete categories. This means that in a histogram there are no gaps between the columns representing the different categories.

The height of competitors are continuous data. There are no gaps between the data. 
Even the train timings are continuous data.   
Hence, option B and C are correct.

An ogive curve is 

  1. Histogram

  2. Frequency polygon

  3. Cumulative frequency

  4. All the above


Correct Option: A

Draw the histogram and use it to find the mode for the following frequency distribution.

House - Rent in Rs. per month $4000 - 6000$ $6000 - 8000$ $8000 - 10000$ $10000 - 12000$
Number of families $200$ $240$ $300$ $50$
  1. Rs. $8000$

  2. Rs. $8350$

  3. Rs. $8500$

  4. Rs. $8750$


Correct Option: B
Explanation:
max. frequency = $300$
so group is = $8000-10000$
so mode = $L+\dfrac{f _{1}-f _{0}}{2f _{1}-f _{0}-f _{2}}\times w$
$L$= lower class boundary of the modal group
$f _{1}$ = frequency of the modal group
$f _{0}$= frequency of the class preceding or just before the modal class
$f _{2}$ = frequency of the class succeeding or just after the modal class
$w$= group width
mode = $8000+ \dfrac{300-240}{2\times 300-240-50}\times 2000$
mode= $8000+387.096$
mode = $8387.096$
mode = $8350$

Represent the following data by histogram and hence compute mode.

Price of sugar per kg (in Rs.) 18 - 20 20 - 22 22 - 24 24 - 26 26 - 28 Total
Number of weeks 4 8 22 12 6 52
  1. 21.2 Rs.

  2. 22.2 Rs.

  3. 23.2 Rs.

  4. 24.2 Rs.


Correct Option: C
Explanation:
max. frequency = $22$
so group is = $22-24$
so mode = $L+\dfrac{f _{1}-f _{0}}{2f _{1}-f _{0}-f _{2}}\times w$
$L$= lower class boundary of the modal group
$f _{1}$ = frequency of the modal group
$f _{0}$= frequency of the class preceding or just before the modal class
$f _{2}$ = frequency of the class succeeding or just after the modal class
$w$= group width
mode = $22+ \dfrac{22-8}{2\times 22-8-12}\times 2$
mode= $22+1.167$
mode = $23.167$
mode = $23.2$

The diagram used to estimate mode of continuous frequency distribution graphically is _____

  1. histogram

  2. frequency curve

  3. bar diagram

  4. all of these


Correct Option: A
Explanation:

It is fundamental concept that histogram is used to obtain mode from continuous frequency distribution graphically.

Represent the following data using histogram, hence find the mode.

Height of students (cm) 140 - 144 145 - 149 150 - 154 155 - 159
Number of students 2 12 10 4
  1. $146\  cm$

  2. $147\  cm$

  3. $149\  cm$

  4. $150\  cm$


Correct Option: B
Explanation:
max. frequency = $12$
so group is = $145-149$
so mode = $L+\dfrac{f _{1}-f _{0}}{2f _{1}-f _{0}-f _{2}}\times w$
$L$= lower class boundary of the modal group
$f _{1}$ = frequency of the modal group
$f _{0}$= frequency of the class preceding or just before the modal class
$f _{2}$ = frequency of the class succeeding or just after the modal class
$w$= group width
mode = $145+ \dfrac{12-2}{2\times 12-2-10}\times 4$
mode= $145+3.333$
mode = $148.333$
mode = $147$

For which of these would you use a histogram to show the data?

  1. The number of letters for different areas in a postman's bag.

  2. The height of competitors in an athletics meet

  3. The number of cassettes produced by 5 companies

  4. The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. from a station.


Correct Option: A

The shoppers who come to a departmental store are marked as : man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning.
W W W G B W W M G G M M W W W
W G B M W B G G M W W M M W W
W M W B W G M W W W W G W M M
W W M W G W M G W M M B G  G W

The mode shoppers are: 

  1. Women

  2. Men

  3. Boy

  4. Girl


Correct Option: A
Explanation:

From the question we are going to form frequency table :

$Shoppers$  $No.\,of\,shoppers$ 
$M$  $15$ 
$W$  $28$ 
$B$  $5$ 
$G$  $12$ 

From table we can see, $Women(W)$ has maximum number of shoppers.

$\therefore$  The mode shoppers are $=Women$

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