18 multiple-choice (MCQ / objective) questions from this chapter, in every exam-style shape used in the paper. Every question comes with an explanation along with the answer, so you remember why the option is correct, not just which one it is.
1 Direct Questions
Direct Questions
- 1 markAccording to the chapter, which three families of statistical techniques are used to analyse data?
(A) Only Measures of Central Tendency(B) Only classification and tabulation(C) Measures of Central Tendency, Measures of Dispersion and Measures of Relationship(D) Only graphical representation - 1 markWhy is the number denoting central tendency called the representative figure of a data set?
(A) Because it is always the highest value in the set(B) Because it is always the lowest value in the set(C) Because it is the point about which items have a tendency to cluster(D) Because it lies at one extreme of the distribution - 1 markThe mean is defined as:
(A) The value occurring most frequently in a distribution(B) The middle value of an arranged series(C) The value derived by summing all the values and dividing it by the number of observations(D) The average of the highest and lowest values - 1 markThe operation of reducing values to smaller numbers by subtracting the assumed mean is called:
(A) Classification(B) Tabulation(C) Graphing(D) Coding - 1 markFind the mode of the following data: 4, 7, 9, 7, 11, 7, 3.
(A) 4(B) 7(C) 9(D) 11
2 Assertion-Reason
Assertion-Reason
- 1 markAssertion (A): The median of a data set is not affected by extreme values.
Reason (R): In an arranged series, the median is determined by the rank/position of an item, not by the actual magnitude of that item.
(A) Both A and R are true, and R is the correct explanation of A(B) Both A and R are true, but R is not the correct explanation of A(C) A is true, but R is false(D) A is false, but R is true - 1 markAssertion (A): The indirect method is normally used to compute the mean for a large number of observations.
Reason (R): The indirect method reduces the values of the observations to smaller numbers by subtracting a constant value from them.
(A) Both A and R are true, and R is the correct explanation of A(B) Both A and R are true, but R is not the correct explanation of A(C) A is true, but R is false(D) A is false, but R is true - 1 markAssertion (A): In a normal distribution, the mean, median and mode are all different values.
Reason (R): A normal distribution is perfectly symmetrical.
(A) Both A and R are true, and R is the correct explanation of A(B) Both A and R are true, but R is not the correct explanation of A(C) A is true, but R is false(D) A is false, but R is true
3 Match the Following
Match the Following
- 1 markMatch List-I (measure/term) with List-II (definition/symbol):
(i) Mean (ii) Median (iii) Mode (iv) Assumed mean
1) Z or M0 2) The middle-ranking item of an arranged series 3) The simple arithmetic average of all values 4) The constant subtracted from every value in the indirect method
(A) (i)-1, (ii)-4, (iii)-2, (iv)-3(B) (i)-2, (ii)-3, (iii)-4, (iv)-1(C) (i)-4, (ii)-1, (iii)-3, (iv)-2(D) (i)-3, (ii)-2, (iii)-1, (iv)-4 - 1 markMatch List-I (mode category) with List-II (feature):
(i) Unimodal (ii) Bimodal (iii) Trimodal (iv) Without mode
1) No value is repeated 2) Three values share an equal, highest frequency 3) Only one value has the highest frequency 4) Two values share an equal, highest frequency
(A) (i)-1, (ii)-2, (iii)-3, (iv)-4(B) (i)-4, (ii)-3, (iii)-1, (iv)-2(C) (i)-3, (ii)-4, (iii)-2, (iv)-1(D) (i)-2, (ii)-1, (iii)-4, (iv)-3
4 Statement-Based Questions
Statement-Based Questions
- 1 markConsider the following statements:
Statement I: The mean is obtained by dividing the sum of all values by the number of observations.
Statement II: Arranging the data in order is not necessary while computing the median.
(A) Only Statement I is correct(B) Only Statement II is correct(C) Both statements are correct(D) Both statements are incorrect - 1 markConsider the following statements:
Statement I: The assumed mean is always taken as the very first value of the series.
Statement II: Computation is minimised when the assumed mean is chosen as close as possible to the middle of the series.
(A) Only Statement I is correct(B) Only Statement II is correct(C) Both statements are correct(D) Both statements are incorrect
5 Arrange in the Correct Order
Arrange in the Correct Order
- 1 markArrange the following steps of computing the mean of grouped data by the direct method in the correct order:
(i) Multiply each midpoint by its corresponding frequency (ii) Find the midpoint of each class interval (iii) Add up all the fx values to get Σfx (iv) Divide Σfx by N
(A) Find midpoints → Multiply by frequency → Sum the fx values → Divide by N(B) Multiply by frequency → Find midpoints → Sum the fx values → Divide by N(C) Sum the fx values → Divide by N → Multiply by frequency → Find midpoints(D) Divide by N → Sum the fx values → Multiply by frequency → Find midpoints
6 Fill in the Blanks
Fill in the Blanks
- 1 markIn Example 2.3, the median height of the mountain peaks in the Himalayas is ________ m.
(A) 8,126(B) 8,598(C) 8,848(D) 8,172
7 Odd One Out
Odd One Out
- 1 markWhich of the following is NOT a measure of central tendency?
(A) Dispersion(B) Mean(C) Median(D) Mode - 1 markWhich of the following is NOT a feature of a normal distribution, as described in the chapter?
(A) The mean lies at the extreme left of the distribution(B) A symmetrical curve(C) Mean = Median = Mode(D) A bell-shaped curve
8 Passage-Based Questions
Passage-Based Questions
Passage
The measurable characteristics such as rainfall, elevation, density of population, levels of educational attainment or age groups vary. If we want to understand them, how would we do ? We may, perhaps, require a single value or number that best represents all the observations. This single value usually lies near the centre of a distribution rather than at either extreme.
- 1 mark(Based on the passage) According to the passage, where does the single representative value usually lie in a distribution?
(A) Near the centre of the distribution(B) At one extreme of the distribution(C) Always at the highest value(D) Always at the lowest value
9 True / False
True / False
- 1 markChoose the correct combination of statements:
(i) The median is not affected by extreme values
(ii) Data must be arranged in order to compute the mean
(iii) The mode is symbolised as Z or M0
(A) Only (i) and (ii)(B) Only (i) and (iii)(C) Only (ii) and (iii)(D) All are correct
Answer Key and Explanations
Direct Questions
- (C) The chapter opens by naming exactly these three techniques used to analyse data.
- (C) The chapter explains it is the representative figure because it is the point about which items have a tendency to cluster.
- (C) The chapter’s own definition: the mean is the value derived by summing all values and dividing by the number of observations.
- (D) The chapter states plainly: ‘Such an operation is known as coding.’
- (B) 7 occurs three times, more often than any other value, so the mode is 7.
Assertion-Reason
- (A) Both A and R are true. Because the median is a positional average, it is unaffected by extreme values: R is the correct explanation of A.
- (A) Both A and R are true: the indirect method is preferred for large numbers of observations precisely because subtracting a constant (the assumed mean) reduces the values to smaller, easier numbers.
- (D) A is false: in a normal distribution the three measures coincide (are equal), they are not different. R is true, and is in fact the very reason the three measures coincide.
Match the Following
- (D) Mean = simple arithmetic average (3); Median = middle-ranking item (2); Mode = Z/M0 (1); Assumed mean = subtracted constant of the indirect method (4).
- (C) Unimodal = one value with highest frequency (3); Bimodal = two values (4); Trimodal = three values (2); Without mode = no value repeated (1).
Statement-Based Questions
- (A) Statement I matches the definition of the mean exactly. Statement II is false: arranging the data in ascending or descending order is essential for locating the median.
- (B) Statement I is false: the assumed mean is preferably chosen near the middle of the series, not the first value. Statement II is true.
Arrange in the Correct Order
- (A) Midpoints are found first, then multiplied by frequency (fx), then the fx values are summed, and finally the sum is divided by N.
Fill in the Blanks
- (D) The arranged series (7,817; 8,076; 8,126; 8,172; 8,598; 8,611; 8,848) has 8,172 m as its 4th item, which is the median.
Odd One Out
- (A) Mean, median and mode are the three measures of central tendency; dispersion is a separate family of measures dealing with the spread of the data.
- (A) A normal distribution is symmetrical, bell-shaped, and has mean=median=mode at its centre; a mean pulled to the extreme left is a feature of a skewed (not normal) distribution.
Passage-Based Questions
- (A) The passage states that this single value usually lies near the centre of a distribution rather than at either extreme.
True / False
- (B) (i) and (iii) are correct. (ii) is false: arranging the data in order is needed for the median, not the mean, which only requires summing all values and dividing by N.
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