30 extra multiple-choice questions for Statistical Techniques (12th Standard Geography, Samacheer Kalvi), beyond the ones printed in the textbook — each with the correct option highlighted and a clear, worked explanation. Free to read in English and Tamil.
Q1
According to the lesson Statistical Techniques, statistics is a branch of science which deals with
- A. qualitative data only
- B. quantitative dataCorrect
- C. rock formations
- D. population migration
Explanation. The lesson opens by defining statistics as a branch of science which deals with quantitative data, and says it includes four processes: collection, presentation, analysis and interpretation of data.
Q2
Arrange the four processes included in statistics in the order given in the lesson.
1. Analysis of data
2. Collection of data
3. Interpretation of data
4. Presentation of data
- A. 2, 4, 1, 3Correct
- B. 2, 1, 4, 3
- C. 4, 2, 1, 3
- D. 2, 4, 3, 1
Explanation. The book lists the four processes as collection of data, presentation of data, analysis of data and interpretation of data, which gives the order 2, 4, 1, 3.
Q3
The language spoken by a person, such as Tamil, Telugu, Hindi or English, is an example of
- A. quantitative data
- B. secondary data
- C. qualitative dataCorrect
- D. grouped data
Explanation. Qualitative data only describes an item, for example coconut tree, palm tree or the language spoken. Quantitative data has a numerical value, such as marks obtained.
Q4
Statistical material which the investigator collects by going from door to door for the purpose of his or her study is called
- A. secondary data
- B. published data
- C. grouped data
- D. primary dataCorrect
Explanation. Primary data are those statistical materials which the investigator collects by going from door to door for his or her study. Secondary data are already collected and recorded by someone else.
Q5
Which of the following statements about types of data is/are correct?
1. Qualitative data gives a numerical value to the item.
2. Secondary data are already collected and recorded data taken from published or unpublished sources.
3. Marks obtained such as 45, 70 and 60 are quantitative data.
- A. 1 only
- B. 1 and 2 only
- C. 2 and 3 onlyCorrect
- D. 1, 2 and 3
Explanation. Statement 1 is wrong: qualitative data only describes an item, while quantitative data has a numerical value such as marks of 45, 70 and 60. Secondary data come from published or unpublished sources.
Q6
Find the odd one out with respect to the methods of primary data collection.
- A. Direct personal investigation
- B. Indirect oral investigation
- C. Published sourcesCorrect
- D. Questionnaire method
Explanation. The book lists three methods of primary data collection: direct personal investigation (interview), indirect oral investigation and the questionnaire method. Published and unpublished sources are methods of secondary data collection.
Q7
What is the range of the data 2, 6, 4, 9, 12, 8, 5, 8?
- A. 8
- B. 12
- C. 6
- D. 10Correct
Explanation. Range = highest value - lowest value. Here the highest value is 12 and the lowest is 2, so the range is 12 - 2 = 10.
Q8
When numerical raw data is arranged in ascending or descending order, it is called
- A. an arrayCorrect
- B. a class
- C. a tally
- D. a range
Explanation. In statistics, array refers to an orderly arrangement. The lesson states that when numerical raw data is arranged in ascending or descending order, it is called an array (frequency array).
Q9
An arrangement of data into classes is known as
- A. range
- B. frequency distributionCorrect
- C. array
- D. median
Explanation. The lesson defines frequency distribution as an arrangement of data into classes. Class, class limit, midpoint, class interval, tally marks and frequency are its technical terms.
Q10
While using tally marks, how is the fifth observation in a group shown?
- A. By a fifth vertical bar
- B. By a circle around four bars
- C. By a cross stroke over the four barsCorrect
- D. By starting a new column
Explanation. Tally marks come in groups of five. A vertical bar is put for each observation, and after four bars a cross stroke is put for the fifth observation, which makes counting frequencies easy.
Q11
Match the terms with their meanings.
a) Class limit - i) Aggregate of all class frequencies
b) Midpoint - ii) Extreme values of a class
c) Class interval - iii) Sum of the lower and upper limits divided by 2
d) Total frequency - iv) Difference between the upper and lower limits
Codes give the matches for a, b, c, d in order.
- A. iii, ii, iv, i
- B. ii, iii, i, iv
- C. ii, iii, iv, iCorrect
- D. iv, iii, ii, i
Explanation. Class limits are the extreme values of a class; the midpoint is (lower + upper limit)/2; the class interval is upper limit minus lower limit; total frequency is the aggregate of all class frequencies.
Q12
What is the midpoint of the class 40 - 50?
- A. 10
- B. 45Correct
- C. 40
- D. 90
Explanation. The midpoint is obtained by dividing the sum of the lower limit and the upper limit by 2. For the class 40 - 50 it is (40 + 50)/2 = 90/2 = 45.
Q13
Assertion (A): The average is frequently referred to as a measure of central tendency.
Reason (R): Since an average represents the entire data, its value lies somewhere between the largest and the smallest observation.
- A. Both A and R are true and R is the correct explanation of ACorrect
- 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
Explanation. The lesson says an average represents the entire data, so its value lies between the two extremes, the largest and smallest observations. For this reason the average is called a measure of central tendency.
Q14
Find the odd one out with respect to the types of averages given in the lesson.
- A. Mean
- B. Median
- C. Mode
- D. RangeCorrect
Explanation. The lesson names three types of averages: mean, median and mode. Range is the difference between the highest and lowest values, found while organising data, and is not an average.
Q15
The value obtained by dividing the sum of the values of all the given items by the number of items is also called the
- A. assumed mean
- B. arithmetic meanCorrect
- C. median
- D. modal class
Explanation. Mean is defined as the value obtained by dividing the sum of values of all the given items by the number of items. The lesson says it is also called the arithmetic mean: mean = sum of values / N.
Q16
The twelve monthly average temperatures of Cuddalore district add up to 341.09 °C. What is the mean annual temperature?
- A. 31.01 °C
- B. 34.11 °C
- C. 28.42 °CCorrect
- D. 29.34 °C
Explanation. Mean = sum of values / number of items. In Example 13.1 of the lesson, \( \bar{X} = 341.09/12 = 28.42 \), so the mean annual temperature of Cuddalore district is 28.42 °C.
Q17
In the formula for the mean of grouped data, \( \bar{X} = A + \frac{\Sigma fd}{N} \times i \), what does A stand for?
- A. Assumed meanCorrect
- B. Area of the class
- C. Arithmetic total
- D. Actual frequency
Explanation. In this formula A is the assumed mean, f the frequency, i the class size, d the deviation from the assumed mean, \( d = (x - A)/i \), and N the total frequency.
Q18
In finding the mean of grouped data, the assumed mean A = 25 and the class size i = 10. What is the deviation d for the class 40 - 50, whose midpoint is 45?
- A. 20
- B. 2Correct
- C. 4.5
- D. -2
Explanation. The book uses \( d = (x - A)/i \). For the class 40 - 50, x = 45, so d = (45 - 25)/10 = 20/10 = 2, as in the table of Example 13.2.
Q19
For the heights of plants in a garden, A = 25, \( \Sigma fd = 50 \), N = 50 and i = 10. Using \( \bar{X} = A + \frac{\Sigma fd}{N} \times i \), the mean height is
- A. 26 cm
- B. 50 cm
- C. 25 cm
- D. 35 cmCorrect
Explanation. \( \bar{X} = 25 + (50/50) \times 10 = 25 + 1 \times 10 = 35 \). This is the answer worked out in Example 13.2 of the lesson.
Q20
Which measure of central tendency is the middle value of a series arranged in ascending or descending order?
- A. Mean
- B. Mode
- C. MedianCorrect
- D. Range
Explanation. Median is the middle value of a series arranged in any order, ascending or descending. The lesson adds that the median divides the series into two equal parts.
Q21
Twelve monthly temperatures are arranged in ascending order. Using M = value of the \( \left(\frac{N+1}{2}\right) \)th item, the median is
- A. the value of the 6th item
- B. the value of the 7th item
- C. the average of the 6th and 7th itemsCorrect
- D. the average of the 1st and 12th items
Explanation. With N = 12, (12 + 1)/2 = 6.5, so the median is the 6.5th item: (6th item + 7th item)/2. In Example 13.3 this gives (24.6 + 25.6)/2 = 25.1 for Chennai.
Q22
The monthly average rainfall (mm) of Chennai district is 15.54, 10.44, 12.48, 20.96, 57.1, 41.24, 64.4, 99.28, 147.17, 204.22, 165.07 and 133.76. What is the median rainfall?
- A. 49.17 mm
- B. 60.75 mmCorrect
- C. 52.82 mm
- D. 64.4 mm
Explanation. In ascending order: 10.44, 12.48, 15.54, 20.96, 41.24, 57.1, 64.4, 99.28, ... The median is the 6.5th item = (57.1 + 64.4)/2 = 121.5/2 = 60.75 mm.
Q23
In the exercise data of Chennai's monthly rainfall, the highest value is 204.22 mm (October) and the lowest is 10.44 mm (February). What is the range?
- A. 193.78 mmCorrect
- B. 188.68 mm
- C. 214.66 mm
- D. 107.33 mm
Explanation. Range = highest value - lowest value = 204.22 - 10.44 = 193.78 mm. Range is the difference between the two extreme values of the data.
Q24
In the formula for the median of grouped data, \( \text{Median} = l + \frac{\frac{N}{2} - m}{f} \times c \), what does m stand for?
- A. Frequency of the median class
- B. Midpoint of the median class
- C. Lower limit of the median class
- D. Cumulative frequency of the class preceding the median classCorrect
Explanation. In the book's formula, l is the lower limit of the median class, N the total frequency, f the frequency of the median class, m the cumulative frequency of the class preceding the median class and c its class interval.
Q25
The value which occurs most frequently in a set of observations is called the
- A. mean
- B. median
- C. modeCorrect
- D. range
Explanation. Mode is the value which occurs most frequently in a set of observations, or the item which repeats itself the greatest number of times.
Q26
Daily wages and number of workers: 0-10: 3, 10-20: 5, 20-30: 7, 30-40: 10, 40-50: 12, 50-60: 15, 60-70: 12, 70-80: 6, 80-90: 2, 90-100: 8. Which is the modal class?
- A. 40 - 50
- B. 50 - 60Correct
- C. 60 - 70
- D. 90 - 100
Explanation. The modal class is the class which has the maximum frequency. The highest frequency here is 15, so 50 - 60 is the modal class, as in Example 13.6.
Q27
In the formula for the mode of grouped data, \( \text{Mode} = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times c \), what does \( f_2 \) stand for?
- A. Frequency of the class preceding the modal class
- B. Frequency of the modal class
- C. Frequency of the class succeeding the modal classCorrect
- D. Total of all frequencies
Explanation. In the book's formula, \( f_1 \) is the frequency of the modal class, \( f_0 \) the frequency of the class preceding it, \( f_2 \) the frequency of the class succeeding it, c the class width and l the lower limit.
Q28
For a modal class 50 - 60, l = 50, \( f_1 = 15 \), \( f_0 = 12 \), \( f_2 = 12 \) and c = 10. Using \( \text{Mode} = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times c \), the mode is
- A. 55Correct
- B. 53
- C. 60
- D. 57.5
Explanation. Mode = 50 + (15 - 12)/(2 x 15 - 12 - 12) x 10 = 50 + (3/6) x 10 = 50 + 5 = 55, as worked out in Example 13.6.
Q29
Monthly income of workers (in thousands) and number of persons: 15-25: 6, 25-35: 11, 35-45: 7, 45-55: 4, 55-65: 4, 65-75: 2, 75-85: 1. Which is the modal class?
- A. 15 - 25
- B. 35 - 45
- C. 25 - 35Correct
- D. 45 - 55
Explanation. The modal class is the class with the maximum frequency. The highest number of persons, 11, falls in the class 25 - 35, so it is the modal class of this exercise data.
Q30
Annual rainfall (cm) and area (sq.m): 0-25: 300, 25-50: 460, 50-75: 650, 75-100: 730, 100-125: 1200, 125-150: 1900, 150-175: 1500, 175-200: 660. N = 7400. Which is the median class?
- A. 100 - 125
- B. 125 - 150Correct
- C. 150 - 175
- D. 75 - 100
Explanation. N/2 = 7400/2 = 3700. Cumulative frequencies are 300, 760, 1410, 2140, 3340, 5240, ... The value 3700 falls in the class whose cumulative frequency is 5240, so 125 - 150 is the median class.
