Tag: histograms for non-uniform class widths

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Multiple choice maths bar graphs histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

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
Reveal answer Fill a bubble to check yourself
B Correct answer
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

Multiple choice maths bar graphs histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

Multiple choice maths bar graphs histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice maths bar graphs histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

Sum of all components in normalized histogram is equal to

  1. $0$
  2. $2$
  3. $100$
  4. $1$
Reveal answer Fill a bubble to check yourself
D Correct answer
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,

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