Class 10 Graphical Representation (Histogram and Ogive) Mock Test (ICSE)

Topics in Graphical Representation (Histogram and Ogive)

• Histograms
• Ogives (cumulative frequency curves)
• Estimating median and quartiles from an ogive
• Estimating mode from a histogram

Graphical Representation (Histogram and Ogive) practice questions with answers

1. Q1Multiple choice·1 mark
   When estimating the mode graphically using a histogram, lines are drawn diagonally from the top corners of the modal rectangle to the top corners of the:

   1. (a)Median and quartile rectangles
   2. (b)Adjacent classes of equal frequencies only
   3. (c)First and last rectangles of the histogram
   4. (d)Preceding and succeeding rectangles
   Show answer and step marks

   1. Correct option: (d) Preceding and succeeding rectangles+1

   Answer: (d)
2. Q2Multiple choice·1 mark
   For a less than ogive, the cumulative frequency is plotted against the:

   1. (a)Upper class limit
   2. (b)Frequency of the class
   3. (c)Mid-value of the class interval
   4. (d)Lower class limit
   Show answer and step marks

   1. Correct option: (a) Upper class limit+1

   Answer: (a)
3. Q3Multiple choice·1 mark
   If $N$ is the total frequency for a given distribution, the lower quartile ($Q_1$) from the ogive is determined by locating the value on the y-axis corresponding to:

   1. (a)$\frac{N}{2}$
   2. (b)$\frac{3N}{4}$
   3. (c)$\frac{N}{4}$
   4. (d)$N$
   Show answer and step marks

   1. Correct option: (c) $\frac{N}{4}$+1

   Answer: (c)
4. Q4Multiple choice·1 mark
   In a histogram representing a continuous grouped frequency distribution with unequal class intervals, the area of each rectangle is proportional to the:

   1. (a)Class mark
   2. (b)Cumulative frequency
   3. (c)Frequency of the class interval
   4. (d)Product of class size and frequency
   Show answer and step marks

   1. Correct option: (c) Frequency of the class interval+1

   Answer: (c)
5. Q5Short answer·2 marks
   State two differences between a histogram and a bar graph.
   Show answer and step marks

   1. First difference, any one of: a histogram represents continuous data grouped in class intervals, while a bar graph represents discrete or categorical data; in a histogram the bars are adjacent with no gaps, while in a bar graph equal gaps are left between bars; in a histogram the width of each bar equals the class width and the area shows the frequency, while in a bar graph the width is arbitrary and only the height matters.+1
   2. Second difference, a different one from the same list.+1

   Answer: Any two of: a histogram shows continuous class-interval data, a bar graph discrete or categorical data; histogram bars have no gaps, bar-graph bars have equal gaps; histogram bar width is the class width (area matters), bar-graph width is arbitrary (only height matters).

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