MCQs / Mathematics / Measures of Central Tendency

Measures of Central Tendency MCQs — Mathematics (page 2)

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.

26. A student scores 80, 70, 90 in subjects with credit hours 3, 2, 1. The weighted mean score is:

  1. 75.33
  2. 80.83
  3. 78.33
  4. 80

Answer: C) 78.33

Explanation: barxw = sum wxsum w = 4706 = 78.33. SLO M-09-C-03 · Application

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27. The mean of 5 numbers is 75. Four of them are 70, 85, 90, 60. The missing number is:

  1. 70
  2. 75
  3. 76
  4. 74

Answer: A) 70

Explanation: Total = 5 75 = 375; missing = 375 - 305 = 70. SLO M-09-C-03 · Application

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28. 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 modal class is:

  1. 30–40
  2. 10–20
  3. 20–30
  4. 0–10

Answer: C) 20–30

Explanation: The modal class has the highest frequency (10). SLO M-09-C-02 · Understanding

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29. 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.) Using Median = l + hf ( n2 - c ), the median is:

  1. 127.33
  2. 124
  3. 130
  4. 120

Answer: B) 124

Explanation: n = 60, n2 = 30. The median class is 120 –130 with l = 120, h = 10, f = 20, c = 22. Median = 120 + 1020(30 - 22) = 124. SLO M-09-C-02 · Understanding

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30. 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 mean of this distribution is:

  1. 50.8
  2. 50
  3. 52.75
  4. 60.8

Answer: A) 50.8

Explanation: Using midpoints x: sum fx = 2540, sum f = 50, so barx = sum fxsum f = 50.8. SLO M-09-C-02 · Understanding

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31. Which average uses every value in the data?

  1. the mode
  2. the class width
  3. the mean
  4. the median

Answer: C) the mean

Explanation: The mean adds every value. SLO M-09-C-03 · Application

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32. 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 mean of this distribution is:

  1. 65
  2. 64
  3. 69
  4. 64.83

Answer: B) 64

Explanation: Using midpoints x: sum fx = 2560, sum f = 40, so barx = sum fxsum f = 64. SLO M-09-C-02 · Understanding

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33. 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.) The modal class is:

  1. 35–40
  2. 25–30
  3. 30–35
  4. 20–25

Answer: C) 30–35

Explanation: The modal class has the highest frequency (14). SLO M-09-C-02 · Understanding

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34. The mean of 4 numbers is 16. Three of them are 12, 18, 15. The missing number is:

  1. 15
  2. 24
  3. 16
  4. 19

Answer: D) 19

Explanation: Total = 4 16 = 64; missing = 64 - 45 = 19. SLO M-09-C-03 · Application

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35. 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.) Using Median = l + hf ( n2 - c ), the median is:

  1. 25
  2. 20
  3. 27.67
  4. 30

Answer: A) 25

Explanation: n = 30, n2 = 15. The median class is 20 –30 with l = 20, h = 10, f = 10, c = 10. Median = 20 + 1010(15 - 10) = 25. SLO M-09-C-02 · Understanding

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36. Shoe sizes sold in a day: 6, 7, 7, 8, 9, 7, 6, 10, 7. The mode is:

  1. 7
  2. 6
  3. 10
  4. 7.4

Answer: A) 7

Explanation: 7 appears most often. SLO M-09-C-03 · Application

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37. House prices in a street are mostly about Rs. 1 crore, but one mansion costs Rs. 20 crore. The best average to describe a typical house is:

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

Answer: A) the median

Explanation: One extreme value pulls the mean up a lot; the median is not affected by it. SLO M-09-C-03 · Application

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38. 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.) The mean of this distribution is:

  1. 33.25
  2. 35.75
  3. 34.71
  4. 32.5

Answer: A) 33.25

Explanation: Using midpoints x: sum fx = 1330, sum f = 40, so barx = sum fxsum f = 33.25. SLO M-09-C-02 · Understanding

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39. Rainfall (mm) over 5 days: 12, 15, 9, 20, 14. The mean daily rainfall is:

  1. 70 mm
  2. 15 mm
  3. 14 mm
  4. 16 mm

Answer: C) 14 mm

Explanation: 705 = 14 mm. SLO M-09-C-03 · Application

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40. The median class is the class that contains the:

  1. highest value
  2. largest frequency
  3. first value
  4. ( n2 ) th value

Answer: D) ( n2 ) th value

Explanation: Use the cumulative frequencies to find where the n2th value falls. SLO M-09-C-02 · Understanding

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41. 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 mean of this distribution is:

  1. 40.75
  2. 37.33
  3. 35
  4. 35.75

Answer: D) 35.75

Explanation: Using midpoints x: sum fx = 1430, sum f = 40, so barx = sum fxsum f = 35.75. SLO M-09-C-02 · Understanding

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42. The modal class of a grouped distribution is the class with the:

  1. smallest width
  2. middle position
  3. highest frequency
  4. largest midpoint

Answer: C) highest frequency

Explanation: Mode = most frequent. SLO M-09-C-02 · Understanding

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43. The mean of grouped data found using midpoints is:

  1. always a whole number
  2. always exact
  3. an estimate
  4. always larger than the median

Answer: C) an estimate

Explanation: The actual values inside each class are not known. SLO M-09-C-02 · Understanding

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44. 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.) Using Median = l + hf ( n2 - c ), the median is:

  1. 70
  2. 60
  3. 67
  4. 63.33

Answer: D) 63.33

Explanation: n = 40, n2 = 20. The median class is 60 –70 with l = 60, h = 10, f = 15, c = 15. Median = 60 + 1015(20 - 15) = 63.33. SLO M-09-C-02 · Understanding

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