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Organizing and Grouping Data Quiz - CBSE Class 8 Mathematics

Free practice quiz: Organizing and Grouping Data (CBSE Class 8 Mathematics). 19 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 19 multiple-choice questions on Organizing and Grouping Data, and 19 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Frequency Tables and Tally Marks

  • Frequency is the number of times a value occurs in the data.
  • Use tally marks to count each value, then write the total count as its frequency.
  • The frequencies added together must equal the total number of observations.
Total frequency
\[\sum f = n\]

Common mistake: Skipping or double-counting values. Tick off each value as you tally it, then check the frequencies add up to n.

Class Intervals and Class Size

  • Large data is grouped into class intervals such as a–b. Here a is the lower limit and b the upper limit.
  • In NCERT's exclusive method, a value equal to the upper limit goes into the next class.
  • Intervals must not overlap, so each value fits in exactly one class.
Class size
\[h = \text{upper limit} - \text{lower limit}\]
Approximate number of classes
\[\text{number of classes} \approx \frac{\text{range}}{h}\]
Class mark (midpoint)
\[\text{class mark} = \frac{\text{lower limit} + \text{upper limit}}{2}\]

Common mistake: Putting a value equal to an upper limit in the lower class when using exclusive intervals like a–b, b–c.

Discrete Versus Continuous Data

  • Discrete data is counted and takes separate values, like the number of pets or books.
  • Continuous data is measured and can take any value in a range, like time, length or mass.

Common mistake: Calling measured data like height discrete just because it is recorded as whole numbers.

Bar Graph, Histogram, Frequency Polygon

  • A bar graph shows categories with equal-width bars that are separated by gaps.
  • A histogram shows grouped continuous data with touching bars. The width is the class size and the height is the frequency.
  • A frequency polygon joins the midpoints of histogram bar tops. It is useful for comparing two data sets.

Common mistake: Leaving gaps between histogram bars, or using a histogram for categories like favourite fruit.

Range, Median, Cumulative Frequency

  • Range shows the spread of data. Median is the middle value after arranging the data in order.
  • Cumulative frequency is a running total of frequencies. Its last value equals the total number of observations.
  • An ogive plots cumulative frequency against upper class limits.
Range
\[\text{Range} = \text{Highest value} - \text{Lowest value}\]
Median, n odd
\[\text{Median} = \left(\frac{n+1}{2}\right)^{\text{th}} \text{ value}\]
Median, n even
\[\text{Median} = \frac{\left(\frac{n}{2}\right)^{\text{th}} + \left(\frac{n}{2}+1\right)^{\text{th}} \text{ values}}{2}\]
Cumulative frequency
\[cf_k = f_1 + f_2 + \cdots + f_k\]

Common mistake: Finding the median without first arranging the data in ascending or descending order.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. A class collected data on the number of siblings each student has. The data is: 0, 1, 2, 1, 3, 2, 1, 0, 2, 1. How many students have 1 sibling?

    Show answer

    Answer: D. 4

    Count the number of times '1' appears in the data set.

  2. A survey was conducted to find the favorite colors of 25 students. The results are: Red-6, Blue-8, Green-4, Yellow-7. Represent this data using a bar graph. Which color has the most votes?

    Show answer

    Answer: B. Blue

    The bar graph will visually show which color has the highest frequency.

  3. Two sets of data have the same mean but different standard deviations. What can you infer about the distribution of the data in each set?

    Show answer

    Answer: B. The dataset with the higher standard deviation has a wider spread.

    Standard deviation measures the spread or dispersion of data. A higher standard deviation implies greater variability.

  4. What is the significance of using a histogram to represent data compared to other methods like bar charts?

    Show answer

    Answer: C. Histograms are better for continuous data, while bar charts are better for discrete or categorical data.

    Histograms are specifically designed for continuous data, showing frequency distributions across ranges.

  5. How can outliers affect the choice of class intervals when creating a histogram?

    Show answer

    Answer: B. Outliers may necessitate wider class intervals to accommodate extreme values.

    Extreme values (outliers) can skew the representation if class intervals are too narrow. Wider intervals are often necessary to accommodate outliers without distorting the overall distribution.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. The heights (in cm) of 10 plants are: 15, 12, 18, 15, 16, 14, 17, 15, 19, 13. Organize this data in a frequency table with groups of 2 cm intervals (e.g., 12-13, 14-15, etc.). How many plants have heights between 14 and 15 cm?
  2. The weights (in kg) of 12 students are: 40, 42, 45, 40, 48, 42, 45, 46, 40, 44, 47, 45. Create a frequency table with intervals of 2kg. In which interval does the highest number of students fall?
  3. Given the data set: 10, 12, 15, 18, 20, 22, 25, 28, 30, 35. Group this data into class intervals of size 5, starting from 10. How many data points fall in the interval 20-24?
  4. Explain the difference between continuous and discrete data with examples relevant to data handling in class 8 mathematics.
  5. The following data represents the daily rainfall (in mm) for a week: 10, 12, 15, 0, 8, 18, 20. Determine the range and the median rainfall.
  6. A researcher wants to analyze the relationship between the number of hours studied and the exam scores of students. What type of graph would be most suitable to represent this data, and why? Justify your choice considering the type of data involved.
  7. The ages of employees at a company are as follows: 25, 28, 30, 35, 35, 38, 40, 42, 45, 45, 48, 50, 52, 55. Create a histogram representing this data. Choose suitable class intervals and explain your choice.
  8. Create a cumulative frequency table and draw an ogive for the following data representing the marks obtained by students in a test: 20, 25, 28, 30, 35, 35, 40, 42, 45, 45, 50, 50, 50, 55, 60. Explain the process of drawing an ogive.
  9. A company collected data on the number of products sold each day for a month. They want to organize this data using suitable class intervals. What factors should they consider when choosing the class intervals?
  10. Explain how the choice of class intervals can affect the interpretation of a histogram.
  11. Compare and contrast the use of bar graphs and histograms in representing data. When would you use one over the other?
  12. Describe a scenario where using a frequency polygon would be more advantageous than using a histogram, and vice versa.
  13. Explain the concept of cumulative frequency and its application in data analysis. How does it help in understanding the distribution of data?
  14. Critically evaluate the limitations of using grouped data for analysis. What information might be lost when data is grouped, and how can these limitations be mitigated?

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