Measures of Central Tendency: Mean, Median, Mode MCQs

Q1. So far 3 scores have been obtained: [8, 12, 10]. What single next score, when included as the (4)th, would make the mean of all 4 scores exactly 12?

• A.18
• B.12
• C.6
• D.30

Answer: A. 18

Q2. So far 4 scores have been obtained: [20, 16, 24, 18]. What single next score, when included as the (5)th, would make the mean of all 5 scores exactly 21?

• A.27
• B.21
• C.6
• D.78

Answer: A. 27

Data from the problem: 4; 20; 16; 24; 18. Target quantity: the unknown asked in the stem. Formula - Required total = 21×.5 = 105. This is the equation that links the given quantities to the unknown (math, chapter 'Statistics'). Numerically: Required total = 21×.5 = 105 → current sum = 78 → next score = 105 - 78 = 27. Consequently the answer is A) 27. Wrong options at a glance: option B) '21' misses the point - The new average is 21; the score needed to reach it is larger; option C) '6' is wrong because Use 5 scores in the target total, not 4; option D) '78' is incorrect: That is the current total, not the required next score.

Q3. So far 5 scores have been obtained: [5, 9, 7, 11, 8]. What single next score, when included as the (6)th, would make the mean of all 6 scores exactly 9?

• A.14
• B.9
• C.5
• D.40

Answer: A. 14

Reading off the stem: 5; 5; 9; 7; 11. We need: the unknown asked in the stem. Governing law - Required total = 9×.6 = 54. This is the equation that links the given quantities to the unknown (math, chapter 'Statistics'). Plugging the values in: Required total = 9×.6 = 54 → current sum = 40 → next score = 54 - 40 = 14. Hence the answer is A) 14. Eliminating the rest: option B) '9' fails since The new average is 9; the score needed to reach it is larger; option C) '5' is wrong because Use 6 scores in the target total, not 5; option D) '40' is incorrect: That is the current total, not the required next score.