MCQs / Mathematics / Measures of Central Tendency

Measures of Central Tendency MCQs — Mathematics

44 multiple-choice questions on Measures of Central Tendency from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

1. A data set has two values that occur most often. It is called:

  1. bimodal
  2. median
  3. skewed
  4. unimodal

Answer: A) bimodal

Explanation: Two modes — bimodal. SLO M-09-C-03 · Application

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2. A government plans to spend 40% of a fund on schools (cost index 120), 35% on hospitals (index 150) and 25% on roads (index 100). The weighted mean cost index is:

  1. 123.3
  2. 130
  3. 125.5
  4. 120

Answer: C) 125.5

Explanation: 0.40 120 + 0.35 150 + 0.25 100 = 48 + 52.5 + 25 = 125.5. SLO M-09-C-03 · Application

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3. Class Frequency ------ 20–25 2 25–30 9 30–35 14 35–40 11 40–45 4 (Classes are continuous: a –b means a le x < b.) Using Median = l + hf ( n2 - c ), the median is:

  1. 35
  2. 36.25
  3. 30
  4. 33.21

Answer: D) 33.21

Explanation: n = 40, n2 = 20. The median class is 30 –35 with l = 30, h = 5, f = 14, c = 11. Median = 30 + 514(20 - 11) = 33.21. SLO M-09-C-02 · Understanding

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4. A student scores 60, 90 in subjects with credit hours 1, 3. The weighted mean score is:

  1. 82.5
  2. 85
  3. 75
  4. 79.5

Answer: A) 82.5

Explanation: barxw = sum wxsum w = 3304 = 82.5. SLO M-09-C-03 · Application

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5. The ages of 5 children are 4, 6, 6, 8 and 11. Which statement is true?

  1. Mean = 6, median = 7, mode = 6
  2. Mean = 6, median = 6, mode = 8
  3. Mean = 7, median = 6, mode = 6
  4. Mean = 7, median = 7, mode = 6

Answer: C) Mean = 7, median = 6, mode = 6

Explanation: 355 = 7; middle value 6; most frequent 6. SLO M-09-C-03 · Application

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6. To find the mean of grouped data, each class is represented by its:

  1. lower limit
  2. midpoint
  3. upper limit
  4. frequency

Answer: B) midpoint

Explanation: We assume the values in a class are centred at its midpoint. SLO M-09-C-02 · Understanding

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7. Class Frequency ------ 40–50 3 50–60 12 60–70 15 70–80 6 80–90 4 (Classes are continuous: a –b means a le x < b.) The modal class is:

  1. 70–80
  2. 50–60
  3. 60–70
  4. 40–50

Answer: C) 60–70

Explanation: The modal class has the highest frequency (15). SLO M-09-C-02 · Understanding

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8. The median of 3, 9, 4, 7, 10, 2 is:

  1. 5.83
  2. 4
  3. 7
  4. 5.5

Answer: D) 5.5

Explanation: Sorted: 2, 3, 4, 7, 9, 10; median = 4 + 72 = 5.5. SLO M-09-C-03 · Application

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9. A shop wants to know which shirt size to stock most. It should use:

  1. the median
  2. the mode
  3. the mean
  4. the range

Answer: B) the mode

Explanation: The mode is the most popular size. SLO M-09-C-03 · Application

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10. The mean of 10 numbers is 24. If 6 is added to each number, the new mean is:

  1. 30
  2. 40
  3. 84
  4. 24

Answer: A) 30

Explanation: Adding the same amount to every value adds it to the mean. SLO M-09-C-03 · Application

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11. A shopkeeper sells 20 kg of rice at Rs. 300/kg and 30 kg at Rs. 350/kg. The average price per kg is:

  1. Rs. 330
  2. Rs. 325
  3. Rs. 650
  4. Rs. 340

Answer: A) Rs. 330

Explanation: Weighted mean = 20(300) + 30(350)50 = 16,50050 = 330. SLO M-09-C-03 · Application

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12. Class Frequency ------ 0–20 6 20–40 10 40–60 16 60–80 12 80–100 6 (Classes are continuous: a –b means a le x < b.) The modal class is:

  1. 60–80
  2. 0–20
  3. 20–40
  4. 40–60

Answer: D) 40–60

Explanation: The modal class has the highest frequency (16). SLO M-09-C-02 · Understanding

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13. Monthly salaries (thousand Rs.): 120, 95, 110, 400, 105. The median salary is:

  1. 110
  2. 305
  3. 95
  4. 166

Answer: A) 110

Explanation: Arrange in order: 95, 105, 110, 120, 400. The middle value is 110. SLO M-09-C-03 · Application

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14. Rainfall (mm) over 6 days: 45, 38, 52, 61, 44, 48. The mean daily rainfall is:

  1. 50 mm
  2. 48 mm
  3. 52 mm
  4. 288 mm

Answer: B) 48 mm

Explanation: 2886 = 48 mm. SLO M-09-C-03 · Application

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15. Monthly salaries (thousand Rs.): 32, 45, 28, 51, 39, 60, 41. The median salary is:

  1. 51
  2. 32
  3. 41
  4. 42.3

Answer: C) 41

Explanation: Arrange in order: 28, 32, 39, 41, 45, 51, 60. The middle value is 41. SLO M-09-C-03 · Application

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16. Class Frequency ------ 10–20 5 20–30 8 30–40 12 40–50 9 50–60 6 (Classes are continuous: a –b means a le x < b.) Using Median = l + hf ( n2 - c ), the median is:

  1. 30
  2. 38.75
  3. 40
  4. 35.83

Answer: D) 35.83

Explanation: n = 40, n2 = 20. The median class is 30 –40 with l = 30, h = 10, f = 12, c = 13. Median = 30 + 1012(20 - 13) = 35.83. SLO M-09-C-02 · Understanding

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17. Class Frequency ------ 10–20 5 20–30 8 30–40 12 40–50 9 50–60 6 (Classes are continuous: a –b means a le x < b.) The modal class is:

  1. 10–20
  2. 20–30
  3. 40–50
  4. 30–40

Answer: D) 30–40

Explanation: The modal class has the highest frequency (12). SLO M-09-C-02 · Understanding

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18. Monthly salaries (thousand Rs.): 15, 22, 18, 30, 25, 20. The median salary is:

  1. 21
  2. 15
  3. 30
  4. 21.7

Answer: A) 21

Explanation: Arrange in order: 15, 18, 20, 22, 25, 30. The middle values are 20 and 22, median = 21. SLO M-09-C-03 · Application

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19. A company forecasts next year's budget as the mean of the last 4 years' budgets: 50, 55, 62 and 69 (million Rs.). The forecast is:

  1. 58.5 million
  2. 62 million
  3. 59 million
  4. 69 million

Answer: C) 59 million

Explanation: 50 + 55 + 62 + 694 = 2364 = 59. SLO M-09-C-03 · Application

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20. Class Frequency ------ 100–110 8 110–120 14 120–130 20 130–140 10 140–150 8 (Classes are continuous: a –b means a le x < b.) The mean of this distribution is:

  1. 125.5
  2. 125
  3. 124.33
  4. 129.33

Answer: C) 124.33

Explanation: Using midpoints x: sum fx = 7460, sum f = 60, so barx = sum fxsum f = 124.33. SLO M-09-C-02 · Understanding

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21. Class Frequency ------ 0–10 4 10–20 6 20–30 10 30–40 7 40–50 3 (Classes are continuous: a –b means a le x < b.) The mean of this distribution is:

  1. 26.5
  2. 29.67
  3. 24.67
  4. 25

Answer: C) 24.67

Explanation: Using midpoints x: sum fx = 740, sum f = 30, so barx = sum fxsum f = 24.67. SLO M-09-C-02 · Understanding

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22. Class Frequency ------ 0–20 6 20–40 10 40–60 16 60–80 12 80–100 6 (Classes are continuous: a –b means a le x < b.) Using Median = l + hf ( n2 - c ), the median is:

  1. 51.25
  2. 60
  3. 40
  4. 53.8

Answer: A) 51.25

Explanation: n = 50, n2 = 25. The median class is 40 –60 with l = 40, h = 20, f = 16, c = 16. Median = 40 + 2016(25 - 16) = 51.25. SLO M-09-C-02 · Understanding

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23. A student scores 65, 85, 75, 90 in subjects with credit hours 4, 3, 2, 1. The weighted mean score is:

  1. 75.5
  2. 72.5
  3. 78.75
  4. 78

Answer: A) 75.5

Explanation: barxw = sum wxsum w = 75510 = 75.5. SLO M-09-C-03 · Application

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24. Class Frequency ------ 100–110 8 110–120 14 120–130 20 130–140 10 140–150 8 (Classes are continuous: a –b means a le x < b.) The modal class is:

  1. 110–120
  2. 120–130
  3. 100–110
  4. 140–150

Answer: B) 120–130

Explanation: The modal class has the highest frequency (20). SLO M-09-C-02 · Understanding

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25. Shoe sizes sold in a day: 38, 40, 39, 40, 41, 40, 42, 39. The mode is:

  1. 40
  2. 39.9
  3. 42
  4. 38

Answer: A) 40

Explanation: 40 appears most often. SLO M-09-C-03 · Application

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