Question

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

Time (t) in minutes
Frequency
5 2
10 9
15 20 WOO
25 a) Work out an estimate for the mean time it took the students.
Round your answer to 2 significant figures.
b) What fraction of the students finished in less than 20 minutes?

Answer 1

a) The mean time it took the students, t ≈ 17.08 minutes

b) The fraction of the students that finished under 20 minutes is 2/3 of the students

Explanation:

a) The mean of the frequency of grouped data is given as follows;

The given data arranged in tabular form is presented as follows;

`\begin{array}{cccc}Time \, (t) \, in \, minutes & Midpoint, m & Frequency, f & Product \ m \cdot f \\5\leq t < 10 & 7.5 & 2 & 15 \\10\leq t < 15 & 12.5 & 9 & 112.5\\15\leq t < 20 & 17.5 & 5 & 87.5 \\20\leq t < 25 & 22.5 & 5 & 112.5 \\25 \leq t < 30 & 27.5 & 3 & 82.5 \\Sum & 87.5 & N = 24 & \Sigma (m\cdot f) = 410 \end{array}`

Therefore, the mean time it took the students = ∑(f·m)/N = 410/24 =
`17(1)/(12)`

The mean time it took the students, t ≈ 17.08 minutes

b) The number of the students that finished under 20 minutes = 2 + 9 + 5 = 16 students

The fraction of the students that finished under 20 minutes = 16/24 of the = 2/3 of the students.