Question

the table shows the time it took a group of students to complete a puzzle

Answer 1

Answer:

a. 17  b. 16/24

Step-by-step explanation:

a. Find the midpoints of each class interval which is:

7.5 x 2 = 15

12.5 x 9 = 112.5

17.5 x 5 = 87.5

22.5 x 5 = 112.5

27.5 x 3 = 82.5

Add all of these up to give 410

Add up the total of the frequency column which is 24

410 / 24 = 17.0833.....

Rounded to 2 significant figures, the answer is 17

b. Add together all the people under 20 which totals to 16 and put this over the total of 24 to give the fraction 16/24

Answer 2

The estimated mean time it took the students and the fraction of students who finished in less than 20 minutes is 17 and 2/3 respectively.

The mean of a grouped distribution can be written as :

• Mean = Σ(F × X) / ΣF
• F = frequency ; x = midpoint

Let's calculate the midpoint :

Midpoint = (Lower + Upper boundary) / 2

X ____ F __ FX

7.5 ___2 __ 15

12.5__ 9 __ 112.5

17.5 __ 5 __ 87.5

22.5 _ 5 __ 112.5

27.5 __3 __ 82.5

_____24 __410

The mean of the distribution = 410 ÷ 24 = 17.08 = 17 minutes

2.) Fraction of students that finished in less than 20 minutes :

Number of students who finished in less than 20 minutes = (2 + 9 + 5) = 16

Total number of students = 20

Fraction that finished in less than 20 minutes = 16/24 = 2/3

Therefore, 2/3 of the students finished in less than 20 minutes.

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