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Introduction to Statistics Quiz - CBSE Class 9 Mathematics

Free practice quiz: Introduction to Statistics (CBSE Class 9 Mathematics). 20 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 9 Mathematics practice quiz has 20 multiple-choice questions on Introduction to Statistics, and 20 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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Data, Types and Frequency

  • Data is a collection of facts, such as numbers or words, gathered to give information.
  • Categorical data are labels or groups (eye colour, blood group). Numerical data are counts or measurements.
  • Discrete data take separate countable values (number of pets). Continuous data can take any value in a range (height).
Total of all frequencies equals number of observations
\[\sum f_i = n\]

Common mistake: Treating number labels like jersey numbers or PIN codes as numerical data. They only name groups, so they are categorical.

Histograms and Box Plots

  • Frequency is how many times a value or class interval occurs in the data.
  • A histogram shows class intervals as touching bars. Each bar's height or area shows that class's frequency.
  • A box plot shows minimum, lower quartile, median, upper quartile and maximum. Dots beyond the whiskers mark outliers.

Common mistake: Leaving gaps between histogram bars like a bar graph. Histogram bars touch because the class intervals are continuous.

Measures of Central Tendency

  • Mean, median and mode each give one value that represents the centre of the data.
  • Mean is the sum divided by count. Median is the middle value of ordered data. Mode occurs most often.
  • Mode tells you which value is most common. Data can have one mode, several modes, or none.
Mean of ungrouped data
\[\bar{x} = \frac{\sum x_i}{n}\]
Mean from a frequency table
\[\bar{x} = \frac{\sum f_i x_i}{\sum f_i}\]
Median position, n odd
\[\left(\frac{n+1}{2}\right)^{\text{th}} \text{ term}\]
Median, n even
\[\frac{\left(\frac{n}{2}\right)^{\text{th}} \text{ term} + \left(\frac{n}{2}+1\right)^{\text{th}} \text{ term}}{2}\]

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

Measures of Spread

  • Spread tells how far the values are scattered. Range, variance and interquartile range measure spread.
  • Variance is the average squared distance from the mean. A high variance means values are widely scattered.
  • The interquartile range is the upper quartile minus the lower quartile. It is the spread of the middle half.
Range
\[\text{Range} = \text{Maximum} - \text{Minimum}\]
Variance
\[\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}\]

Common mistake: Calling mean, median or mode a measure of spread. They measure the centre, not how scattered the data are.

Outliers and Skewness

  • An outlier is a value far from the rest. It may signal an unusual case or an error.
  • The mean uses every value in its sum, so extreme values pull it. The median stays steady.
  • In skewed data the median represents the centre better. Compare mean, median and mode to judge skewness.
Symmetric distribution
\[\text{Mean} = \text{Median} = \text{Mode}\]
Positively (right) skewed
\[\text{Mean} > \text{Median} > \text{Mode}\]
Negatively (left) skewed
\[\text{Mean} < \text{Median} < \text{Mode}\]

Common mistake: Mixing up the skew directions. If the median is greater than the mean, the long tail is on the left, so the data are negatively skewed.

Exam tips

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

Sample questions

  1. Which of the following is a measure of central tendency?

    Show answer

    Answer: A. Mean

    The mean is a measure of central tendency that represents an average value of a set of numbers.

  2. What is the range of the following data set: 3, 7, 9, 15?

    Show answer

    Answer: A. 12

    The range is the difference between the highest and lowest values. In this case, 15 - 3 = 12.

  3. Which is not a measure of spread in statistics?

    Show answer

    Answer: A. Mean

    Mean is a measure of central tendency, not a measure of spread. Range, variance, and standard deviation are measures of spread.

  4. Which of the following is a type of categorical data?

    Show answer

    Answer: C. Color

    Categorical data represents characteristics and can be divided into groups (e.g., colors).

  5. What is a common graphical method to identify outliers in data?

    Show answer

    Answer: B. Box plot

    Box plots visually depict data distribution and highlight outliers, which are data points that fall outside the 'whiskers' of the plot.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. What does the term 'data' refer to in statistics?
  2. How do you find the mode of a dataset?
  3. The median value is described as:
  4. Which of the following datasets is considered categorical?
  5. If the mode in a given data set is 5, what does it tell you about the data?
  6. What does a high variance in a dataset indicate?
  7. If the median is greater than the mean in a data set, the distribution is likely:
  8. When data is presented in a frequency distribution table, what does each entry under 'frequency' represent?
  9. What is a histogram?
  10. Why is the mean sensitive to extreme values?
  11. In a box plot, what does the interquartile range represent?
  12. Which of the following best describes 'discrete data'?
  13. What does an outlier in a dataset typically indicate?
  14. Why might the median be preferred over the mean in skewed distributions?
  15. How can one determine if data is skewed using mean, median, and mode?

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