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Question
The grades obtained by a group of \(20\) IB students are listed below:
Complete the following table for the grades obtained by the students.
[2]
Write down the modal grade obtained by the students.[1]
Calculate the median grade obtained by the students.[2]
One student is chosen at random from the group.
Find the probability that this student obtained either grade \(4\) or grade \(5\).[1]
Answer/Explanation
Markscheme
(A2) (C2)
Notes: Award (A1) for three correct. Award (A0) for two or fewer correct.[2 marks]
\({\text{Mode}} = 6\) (A1)(ft) (C1)[1 mark]
\({\text{Median}} = 4.5\) (M1)(A1)(ft) (C2)
Note: (M1) for attempt to order raw data (if frequency table not used) or (M1) halfway between 10th and 11th result.[2 marks]
\(\frac{7}{{20}}{\text{ }}(0.35{\text{, }}35\% )\) (A1)(ft) (C1)[1 mark]
Question
\(80\) matches were played in a football tournament. The following table shows the number of goals scored in all matches.
Find the mean number of goals scored per match.[2]
Find the median number of goals scored per match.[2]
A local newspaper claims that the mean number of goals scored per match is two. Calculate the percentage error in the local newspaper’s claim.[2]
Answer/Explanation
Markscheme
\(\frac{{0 \times 16 + 1 \times 22 + 2 \times 19 \ldots }}{{80}}\) (M1)
Note: Award (M1) for substituting correct values into mean formula.
1.75 (A1) (C2)[2 marks]
An attempt to enumerate the number of goals scored. (M1)
\(2\) (A1) (C2)[2 marks]
\(\frac{{2 – 1.75}}{{1.75}} \times 100\) (M1)
\(14.3 \% \) (A1)(ft) (C2)
Notes: Award (M1) for correctly substituted \(\% \) error formula. \(\% \) sign not required. Follow through from their answer to part (a). If \(100\) is missing and answer incorrect award (M0)(A0). If \(100\) is missing and answer incorrectly rounded award (M1)(A1)(ft)(AP).[2 marks]
Question
The table shows the number of bicycles owned by 50 households.
Write down the value of
(i) t ;
(ii) w .[2]
Indicate with a tick (
) whether the following statements are True or False.
[4]
Answer/Explanation
Markscheme
(i) 8 (A1)
(ii) 48 (A1)(ft) (C2)
Note: Follow through from their t, even if no workings seen as long as w < 50.
(A1)(A1)(A1)(A1) (C4)
Question
In a particular week, the number of eggs laid by each hen on a farm was counted. The results are summarized in the following table.
State whether these data are discrete or continuous.[1]
Write down
(i) the number of hens on the farm;
(ii) the modal number of eggs laid.[2]
Calculate
(i) the mean number of eggs laid;
(ii) the standard deviation.[3]
Answer/Explanation
Markscheme
discrete (A1) (C1)
(i) 60 (A1)
(ii) 5 (A1) (C2)
(i) \(\frac{{1 \times 4 + 2 \times 7 + 3 \times 12 \ldots }}{{60}}\) (M1)
Notes: Award (M1) for an attempt to substitute into the “mean of a set of data” formula, with at least three correct terms in the numerator.
Denominator must be 60.
Follow through from part (b)(i), only if work is seen.
\( = 4.03{\text{ }}(4.03333 \ldots )\) (A1)
Notes: Award at most (M1)(A0) for an answer of 4 but only if working seen.
(ii) \(1.54{\text{ }}(1.53803 \ldots )\) (A1) (C3)
Question
Two groups of 40 students were asked how many books they have read in the last two months. The results for the first group are shown in the following table.
The quartiles for these results are 3 and 5.
Write down the value of the median for these results.[1]
Draw a box-and-whisker diagram for these results on the following grid.
[3]
The results for the second group of 40 students are shown in the following box-and-whisker diagram.
Estimate the number of students in the second group who have read at least 6 books.[2]
Answer/Explanation
Markscheme
\(4\) (A1)(C1)
(A1)(ft)(A1)(A1) (C3)
Notes: Award (A1)(ft) for correct median, (A1) for correct quartiles and box, (A1) for endpoints 2 and 8 joined by a straight line that does not cross the box. Follow through from their median from part (a).
\(40 \times 0.25\) (M1)
Notes: Award (M1) for \(40 \times 25\% \;\;\;\)OR\(\;\;\;40 – 40 \times 75\% \).
\(10\) (A1) (C2)
Question
The lengths of trout in a fisherman’s catch were recorded over one month, and are represented in the following histogram.
Complete the following table.
[2]
State whether length of trout is a continuous or discrete variable.[1]
Write down the modal class.[1]
Any trout with length 40 cm or less is returned to the lake.
Calculate the percentage of the fisherman’s catch that is returned to the lake.[2]
Answer/Explanation
Markscheme
(A2) (C2)
Note: Award (A2) for all correct entries, (A1) for 3 correct entries.[2 marks]
continuous (A1) (C1)[1 mark]
\({\text{60 (cm)}} < {\text{trout length}} \leqslant {\text{70 (cm)}}\) (A1) (C1)
Note: Accept equivalent notation such as \((60,{\text{ }}70]\) or \(]60,{\text{ }}70]\).
Award (A0) for “60-70” (incorrect notation).[1 mark]
\(\frac{4}{{22}} \times 100\) (M1)
Note: Award (M1) for their 4 divided by their 22.
\( = 18.2{\text{ }}(18.1818 \ldots )\) (A1)(ft) (C2)
Note: Follow through from their part (a). Do not accept 0.181818….[2 marks]
Question
In an international competition, participants can answer questions in only one of the three following languages: Portuguese, Mandarin or Hindi. 80 participants took part in the competition. The number of participants answering in Portuguese, Mandarin or Hindi is shown in the table.
A boy is chosen at random.
State the number of boys who answered questions in Portuguese.[1]
Find the probability that the boy answered questions in Hindi.[2]
Two girls are selected at random.
Calculate the probability that one girl answered questions in Mandarin and the other answered questions in Hindi.[3]
Answer/Explanation
Markscheme
20 (A1) (C1)[1 mark]
\(\frac{5}{{43}}\,\,\,\left( {0.11627 \ldots ,\,\,11.6279 \ldots {\text{% }}} \right)\) (A1)(A1) (C2)
Note: Award (A1) for correct numerator, (A1) for correct denominator.[2 marks]
\(\frac{7}{{37}} \times \frac{{12}}{{36}} + \frac{{12}}{{37}} \times \frac{7}{{36}}\) (A1)(M1)
Note: Award (A1) for first or second correct product seen, (M1) for adding their two products or for multiplying their product by two.
\( = \frac{{14}}{{111}}\,\,\left( {\,0.12612 \ldots ,\,\,12.6126\,{\text{% }}} \right)\) (A1) (C3)[3 marks]