IBDP Maths AI: Topic: SL 4.2: Presentation of data: IB style Questions HL Paper 1

Question

The table below shows the number of words in the extended essays of an IB class.

a.Draw a histogram on the grid below for the data in this table.

[3]

 

b.Write down the modal group.[1]

c.The maximum word count is \(4000\) words.

Write down the probability that a student chosen at random is on or over the word count.[2]

▶️Answer/Explanation

Markscheme

     (A3)     (C3)

Notes: (A3) for correct histogram, (A2) for one error, (A1) for two errors, (A0) for more than two errors.
Award maximum (A2) if lines do not appear to be drawn with a ruler.
Award maximum (A2) if a frequency polygon is drawn.[3 marks]

a.

\({\text{Modal group}} = 3800 \leqslant w < 4000\)     (A1)     (C1)[1 mark]

b.

\({\text{Probability}} = \frac{3}{{35}}{\text{ }}(0.0857{\text{, }}8.57\% )\)     (A1)(A1)     (C2)

Note: (A1) for correct numerator (A1) for correct denominator.[2 marks]

Question

The following histogram shows the weights of a number of frozen chickens in a supermarket. The weights are grouped such that \(1 \leqslant {\text{weight}} < 2\), \(2 \leqslant {\text{weight}} < 3\) and so on.

b.Find the total number of chickens.[1]

c.Write down the modal group.[1]

d.Gabriel chooses a chicken at random.

Find the probability that this chicken weighs less than \(4{\text{ kg}}\).[2]

▶️Answer/Explanation

Markscheme

\(96\)     (A1)     (C1)[1 mark]

b.

\(3 \leqslant {\text{weight}} < 4{\text{ kg}}\) . Accept \(3 – 4{\text{ kg}}\)     (A1)     (C1)[1 mark]

c.

For adding three heights or subtracting \(14\) from \(96\)     (M1)

\(\frac{{82}}{{96}}{\text{ }}(0.854{\text{ or }}\frac{{41}}{{48}}{\text{, }}85.4\% )\) (ft) from (b).     (A1)(ft)     (C2)[2 marks]

d.

Question

a.The distribution of the weights, correct to the nearest kilogram, of the members of a football club is shown in the following table.

On the grid below draw a histogram to show the above weight distribution.

[2]

 

b.Write down the mid-interval value for the \(40 – 49\) interval.[1]

c.Find an estimate of the mean weight of the members of the club.[2]

d.Write down an estimate of the standard deviation of their weights.[1]

▶️Answer/Explanation

Markscheme

     (A1)(A1)     (C2)


Notes: (A1) for all correct heights, (A1) for all correct end points (\(39.5\), \(49.5\) etc.).

Histogram must be drawn with a ruler (straight edge) and endpoints must be clear.
Award (A1) only if both correct histogram and correct frequency polygon drawn. [2 marks]

a.

\(44.5\)     (A1)     (C1)

Note: If (b) is given as \(45\) then award
(b) \(45\)     (A0)
(c) \(58.8{\text{ kg}}\)     (M1)(A1)(ft) or (C2)(ft) if no working seen.
(d) \(8.44\)     (C1)

[1 mark]

b.

Unit penalty (UP) applies in this question.

\({\text{Mean}} = \frac{{44.5 \times 6 + 54.5 \times 18 +  \ldots }}{{42}}\)     (M1)

Note: (M1) for a sum of frequencies multiplied by midpoint values divided by \(42\).

\( = 58.3{\text{ kg}}\)     (A1)(ft)     (C2)

Note: Award (A1)(A0)(AP) for \(58\).


Note:
If (b) is given as \(45\) then award

(b) \(45\)     (A0)
(c) \(58.8{\text{ kg}}\)     (M1)(A1)(ft) or (C2)(ft) if no working seen.
(d) \(8.44\)     (C1)[2 marks]

c.

\({\text{Standard deviation}} = 8.44\)     (A1)     (C1)

Note: If (b) is given as \(45\) then award
(b) \(45\)     (A0)
(c) \(58.8{\text{ kg}}\)     (M1)(A1)(ft) or (C2)(ft) if no working seen.
(d) \(8.44\)     (C1)[1 mark]

d.

Question

120 Mathematics students in a school sat an examination. Their scores (given as a percentage) were summarized on a cumulative frequency diagram. This diagram is given below.

a.Complete the grouped frequency table for the students.

[3]

 

b.Write down the mid-interval value of the \(40 < x \leqslant 60\) interval.[1]

 

c.Calculate an estimate of the mean examination score of the students.[2]

 
▶️Answer/Explanation

Markscheme

      (A1)(A1)(A1)     (C3)[3 marks]

a.

50     (A1)    (C1)[1 mark]

b.

\({\text{Mean}} = \frac{{10 \times 14 + ……. + 90 \times 6}}{{120}}\)     (M1)

Note: Award (M1) for correct substitution of their values from (a) in mean formula.

\( = 45\frac{2}{3}(45.7)\)     (A1)(ft)     (C2)[2 marks]

c.

Question

The weights of 90 students in a school were recorded. The information is displayed in the following table.

a.Write down the mid interval value for the interval \(50 \leqslant w \leqslant 60\).[1]

b.i.Use your graphic display calculator to find an estimate for the mean weight.[2]

b.ii.Use your graphic display calculator to find an estimate for the standard deviation.[1]

c.Find the weight that is 3 standard deviations below the mean.[2]

▶️Answer/Explanation

Markscheme

55     (A1)     (C1)[1 mark]

a.

\(62.\bar 5{\text{ }}\left( {62.6} \right)\)     (A2)(ft)     (C2)[2 marks]

b.i.

8.86     (A1)     (C1)

Note: Follow through from their answer to part (a).[1 mark]

b.ii.

62.6 – 3 × 8.86 = 36.0     (M1)(A1)(ft)     (C2)

Note: Accept 36.

Follow through from their values in part (b) only if working is seen.[2 marks]

c.
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