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NCERT · Class 11 · Statistics

Chapter 4: Presentation of Data

Practice each question, then open the answer or worked solution.

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Textbook exercises

15 questions
Q1Written answer

Bar diagram is a (i) one-dimensional diagram (ii) two-dimensional diagram (iii) diagram with no dimension (iv) none of the above

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Worked solution
ANSWER (i) one-dimensional diagram. In a bar diagram only the height (length) of the bar represents the magnitude of the data; the width of the bar is unimportant. Since only one dimension carries meaning, a bar diagram is a one-dimensional diagram.
Q2Written answer

Data represented through a histogram can help in finding graphically the (i) mean (ii) mode (iii) median (iv) all the above

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Worked solution
ANSWER (ii) mode. A histogram gives the value of the mode of a frequency distribution graphically — the x-coordinate of the dotted vertical line drawn through the tallest rectangle gives the mode.
Q3Written answer

Ogives can be helpful in locating graphically the (i) mode (ii) mean (iii) median (iv) none of the above

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Worked solution
ANSWER (iii) median. The point where the ‘less than’ ogive and the ‘more than’ ogive intersect gives the median of the frequency distribution.
Q4Written answer

Data represented through arithmetic line graph help in understanding (i) long term trend (ii) cyclicity in data (iii) seasonality in data (iv) all the above

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Worked solution
ANSWER (iv) all the above. An arithmetic line graph (time series graph) helps in understanding the long-term trend, cyclicity (periodicity) and seasonality in data over time.
Q5Written answer

Width of bars in a bar diagram need not be equal (True/False).

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Worked solution
ANSWER False. In a bar diagram the bars are equi-width (and equi-spaced). Although the width itself is unimportant for comparison — only height matters — by convention all bars are drawn of equal width.
Q6Written answer

Width of rectangles in a histogram should essentially be equal (True/False).

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Worked solution
ANSWER False. The width of a rectangle in a histogram equals the width of its class interval, and class intervals may be unequal. When widths differ, the heights are adjusted using frequency density so that the areas remain proportional to the frequencies.
Q7Written answer

Histogram can only be formed with continuous classification of data (True/False).

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Worked solution
ANSWER True. A histogram is drawn only for a continuous variable. If the classes are not continuous, they must first be converted into continuous classes (exclusive form) before a histogram can be drawn.
Q8Written answer

Histogram and column diagram are the same method of presentation of data. (True/False)

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Worked solution
ANSWER False. They are different. In a histogram no space is left between rectangles and it is drawn only for continuous variables, where area (not just height) is meaningful. In a column (bar) diagram, spaces are left between bars, it can be used for discrete and continuous data, and only the height matters.
Q9Written answer

Mode of a frequency distribution can be known graphically with the help of histogram. (True/False)

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Worked solution
ANSWER True. A histogram gives the mode graphically; the x-coordinate of the vertical line through the tallest rectangle (located by drawing diagonals at the peak) is the mode.
Q10Written answer

Median of a frequency distribution cannot be known from the ogives. (True/False)

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Worked solution
ANSWER False. The median can be found from ogives — the point of intersection of the ‘less than’ and ‘more than’ ogives gives the median of the distribution.