Kerala SSLC · Mathematics · Class 10

Statistics: Important Questions with Answers

These are 10 important multiple-choice questions from the Kerala SSLC Mathematics chapter “Statistics” (Kerala SCERT syllabus). Each one shows the correct answer and a short explanation of why it is right. Try answering before you read the answer. ExamSummary has 20 practice questions on this chapter in total.

1. Q1.In the step-deviation method for finding the mean, if Σfiui = 0, then the mean is equal to...

   • A)a
   • B)h
   • C)0
   • D)a + h

   Answer: A) a

   The formula for mean is x̄ = a + (Σfiui / Σfi) × h. If the numerator Σfiui is zero, the second term vanishes, leaving the mean equal to the assumed mean 'a'.

2. Q2.To find the median graphically using an Ogive curve, we locate the point of intersection of...

   • A)Two frequency polygons
   • B)Less than and more than cumulative frequency curves
   • C)The x-axis and the y-axis
   • D)The highest and lowest bars

   Answer: B) Less than and more than cumulative frequency curves

   The median corresponds to the x-coordinate where the 'less than' and 'more than' cumulative frequency curves intersect. This intersection point represents the middle value of the dataset.

3. Q3.If the mode of a distribution is 24 and the mean is 12, what is the approximate median according to the empirical relation?

   • A)16
   • B)20
   • C)24
   • D)12

   Answer: A) 16

   Using the empirical formula 3Median = Mode + 2Mean, we calculate 3Median = 24 + 2(12) = 48. Dividing by 3 gives a median value of 16.

4. Q4.What is the class mark of the interval 20-30?

   • A)20
   • B)25
   • C)30
   • D)35

   Answer: B) 25

   The class mark is the midpoint of the upper and lower limits, calculated as (Lower + Upper) / 2. For the interval 20 to 30, the calculation is (20 + 30) / 2 = 25.

5. Q5.Two batches of students have 40 and 60 students with mean marks 50 and 60 respectively. What is the combined mean?

   • A)54
   • B)55
   • C)56
   • D)58

   Answer: C) 56

   The combined mean is the weighted average: ((40 × 50) + (60 × 60)) / (40 + 60) = (2000 + 3600) / 100 = 5600 / 100 = 56.

6. Q6.In a grouped frequency distribution, the modal class is identified by...

   • A)The smallest frequency
   • B)The largest class width
   • C)The class with the maximum frequency
   • D)The first class interval

   Answer: C) The class with the maximum frequency

   The modal class is simply the class interval that contains the highest frequency among all the classes. It indicates the range where the data values are most concentrated.

7. Q7.When drawing a frequency polygon, the vertices are plotted at...

   • A)Upper class limits
   • B)Lower class limits
   • C)Class marks (midpoints)
   • D)Cumulative frequencies

   Answer: C) Class marks (midpoints)

   A frequency polygon is constructed by joining the midpoints (class marks) of the tops of the rectangles in a histogram. These points represent the frequency associated with each class interval.

8. Q8.If every observation in a dataset is increased by 5, how does the mean change?

   • A)Remains unchanged
   • B)Increases by 5
   • C)Increases by 5 times the number of observations
   • D)Decreases by 5

   Answer: B) Increases by 5

   Adding a constant value to every observation shifts the entire distribution without changing its spread. Consequently, the arithmetic mean increases by exactly that same constant value.

9. Q9.In a cumulative frequency table, the value of the last entry always equals...

   • A)The total number of observations
   • B)The class size
   • C)The mean of the data
   • D)The frequency of the last class

   Answer: A) The total number of observations

   The cumulative frequency accumulates the frequencies of all preceding classes up to the current one. Therefore, the final entry represents the sum of all frequencies, which is the total number of observations.

10. Q10.To determine the median class in grouped data, we look for the class where the cumulative frequency is...

    • A)Greater than n
    • B)Just greater than or equal to n/2
    • C)Equal to the total frequency
    • D)Less than n/2

    Answer: B) Just greater than or equal to n/2

    The median class is defined as the class interval containing the n/2-th observation. We select the first class whose cumulative frequency is greater than or equal to half the total number of observations.

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