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Stage 9 - Q1 - 4 marks
20227

Use the outer occupied class boundaries to estimate the range. Explain why it is not the actual attained range.

Time (min)
Frequency
\(5\le t<10\)
0
\(10\le t<15\)
10
\(15\le t<20\)
18
\(20\le t<25\)
8
\(25\le t<30\)
5
Hint

An empty end class contains no possible extreme observation.

Stage 9 - Q2 - 5 marks
20228

Estimate the mean time to 1 decimal place. Show midpoint products and explain why the answer is an estimate.

Time (min)
Frequency
\(0\le t<5\)
6
\(5\le t<10\)
9
\(10\le t<15\)
13
\(15\le t<20\)
22
\(20\le t<25\)
10
Hint

Every class midpoint is repeated as many times as its frequency.

Stage 9 - Q3 - 5 marks
20229

Estimate the mean to 1 decimal place and the range from occupied outer class boundaries. Label both answers as estimates.

Time (min)
Frequency
\(0\le t<10\)
6
\(10\le t<20\)
13
\(20\le t<30\)
11
\(30\le t<40\)
7
\(40\le t<50\)
4
Hint

The mean uses every frequency; the range estimate uses the occupied extremes.

Stage 9 - Q4 - 4 marks
20230

Estimate the combined time for all observations, then the mean time. Give the mean to 1 decimal place.

Time (min)
Frequency
\(15\le t<25\)
14
\(25\le t<35\)
15
\(35\le t<45\)
12
\(45\le t<55\)
9
\(55\le t<65\)
6
Hint

Do not divide until the question asks for a mean.

Stage 9 - Q5 - 4 marks
20231

A pupil averages the five class midpoints and reports \(40\) minutes. Explain the flaw and calculate the correct estimated mean.

Time (min)
Frequency
\(15\le t<25\)
5
\(25\le t<35\)
8
\(35\le t<45\)
16
\(45\le t<55\)
10
\(55\le t<65\)
6
Hint

A class with twenty observations must count more than a class with two.

Stage 9 - Q6 - 5 marks
20232

Compare the two estimated mean times to 1 decimal place using matching class midpoints.

Time (min)
A
B
\(10\le t<15\)
6
7
\(15\le t<20\)
12
10
\(20\le t<25\)
20
20
\(25\le t<30\)
10
12
\(30\le t<35\)
7
6
Hint

Use the same midpoints but different frequencies.

Stage 9 - Q7 - 5 marks
20233

The midpoint estimate of the mean is exactly 30 minutes. Find the missing frequency in the table.

Time (min)
Frequency
\(10\le t<20\)
3
\(20\le t<30\)
?
\(30\le t<40\)
18
Hint

The unknown frequency changes the total number of observations as well as the total midpoint products.

Stage 9 - Q8 - 5 marks
20234

Compare the two estimated mean times to 1 decimal place using matching class midpoints.

Time (min)
A
B
\(5\le t<10\)
8
6
\(10\le t<15\)
15
9
\(15\le t<20\)
13
13
\(20\le t<25\)
9
15
\(25\le t<30\)
6
8
Hint

Use the same midpoints but different frequencies.

Stage 9 - Q9 - 5 marks
20235

The midpoint estimate of the mean is exactly 25 minutes. Find the missing frequency in the table.

Time (min)
Frequency
\(5\le t<15\)
10
\(15\le t<25\)
?
\(25\le t<35\)
33
Hint

The unknown frequency changes the total number of observations as well as the total midpoint products.

Stage 9 - Q10 - 7 marks
20236

Times in minutes are grouped as \(0\le t<10\), \(10\le t<20\), \(20\le t<30\) with frequencies 2,3,5. Find the midpoint mean estimate and the tight interval guaranteed to contain the true mean. Can the estimate be above or below the true mean?

Hint

Replace every hidden value by its class lower bound, then by its upper bound, to bound the total.

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