Consider the following data set that denotes the time (in minutes) taken by a group of teenagers to solve a particular puzzle in order to determine their IQ level: 8, 13, 21, 9, 15, 29, 6, 13, 24, 27, 3, 22, 21, 20, 21, 20, 8, 27, 10, 17, 9, 7, 13, 15, 14, 23, 11, 20, 12, 21, 11, 27, 29, 3, 6, 6, 18, 8, 17, 6, 5, 11, 24, 22, 19, 20, 22, 21, 8, 20, 17, 28, 13, 4, 7, 24, 23, 16, 19, 29, 16, 20, 21, 23, 8, 1, 11, 16, 9, 16, 13, 10, 17, 18, 28, 10, 23, 27, 16, 8, 14, 9, 9, 18, 14, 21, 28, 16, 20, 11, 26, 7, 5, 25, 29, 27, 17, 24, 23, 27, 13, 3, 7, 27, 28, 18, 7, 9, 13, 9, 5, 27, 26, 27, 9, 4, 7, 10, 19, 19, 13, 9, 20, 16, 27, 20, 3, 26, 23, 11, 28, 21, 5, 19, 11, 18, 12, 22, 9, 11, 5, 28, 3, 12, 9, 11, 8, 17, 6, 11 Mention the suitable tools for each of the following cases and with the help of those tools determine the following: (i) The nature of the data provided. (1) (ii) The least and the greatest time needed to complete the puzzle and hence the range of the time required. (3) (iii) How many people completed the puzzle in exact 17 minutes? (2) (iv) What percentage of people completed the puzzle in less than 10 minutes? (2) (v) What is the amount of time required by majority of people to complete the puzzle? (3) (vi) What is the average time score of the group? (3) (vii) If a time span of less than 15 minutes is considered to be a case of high intelligence, how many people in the group are highly intelligent? (2) (viii) How many people took more than 15 minutes but less than 30 minutes to solve the puzzle? (2) (ix) What conclusion can you derive in general regarding the intelligence of the teenage group under study? What can you say about the consistency or inconsistency of the data set provided? Validate your answer with suitable explanation. (1+5+1)
Answers
Solution :-
→ 1 minutes = 1
→ 3 minutes = 5
→ 4 minutes = 2
→ 5 minutes = 5
→ 6 minutes = 5
→ 7 minutes = 6
→ 8 minutes = 7
→ 9 minutes = 11
→ 10 minutes = 4
→ 11 minutes = 10
→ 12 minutes = 3
→ 13 minutes = 8
→ 14 minutes = 3
→ 15 minutes = 2
→ 16 minutes = 7
→ 17 minutes = 6
→ 18 minutes = 5
→ 19 minutes = 5
→ 20 minutes = 9
→ 21 minutes = 8
→ 22 minutes = 4
→ 23 minutes = 6
→ 24 minutes = 4
→ 25 minutes = 1
→ 26 minutes = 3
→ 27 minutes = 10
→ 28 minutes = 6
→ 29 minutes = 4
so,
→ Least time = 1 minute
→ Greatest time = 29 minutes .
→ Range = 29 - 1 = 28 minutes .
→ Total people = 150 .
→ Number of people completed the puzzle in exactly 17 minutes = 6
→ Average time score = 433/28 = 15.5 minutes .
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