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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?

The table shows the time it took a group of students to complete a puzzle. Time (t-example-1

1 Answer

6 votes

Answer:

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 &amp; Midpoint, m &amp; Frequency, f &amp; Product \ m \cdot f \\5\leq t < 10 &amp; 7.5 &amp; 2 &amp; 15 \\10\leq t < 15 &amp; 12.5 &amp; 9 &amp; 112.5\\15\leq t < 20 &amp; 17.5 &amp; 5 &amp; 87.5 \\20\leq t < 25 &amp; 22.5 &amp; 5 &amp; 112.5 \\25 \leq t < 30 &amp; 27.5 &amp; 3 &amp; 82.5 \\Sum &amp; 87.5 &amp; N = 24 &amp; \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.

User Bill Weinman
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