| Date | May 2013 | Marks available | 2 | Reference code | 13M.1.sl.TZ2.14 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Calculate | Question number | 14 | Adapted from | N/A |
Question
The number of passengers in the first ten carriages of a train is listed below.
6 , 8 , 6 , 3 , 8 , 4 , 8 , 5 , p , p
The mean number of passengers per carriage is 5.6.
Calculate the value of p.
Find the median number of passengers per carriage.
If the passengers in the eleventh carriage are also included, the mean number of passengers per carriage increases to 6.0.
Determine the number of passengers in the eleventh carriage of the train.
Markscheme
\(\frac{{48 + 2p}}{{10}} = 5.6\) (M1)
Notes: Accept equivalent forms. Award (M1) for correct substitutions in mean formula.
4 (A1) (C2)
Correctly rearranging the list with their p (M1)
5.5 (A1)(ft) (C2)
Note: Follow through from their value of p in part (a).
\(\frac{{56 + x}}{{11}} = 6.0\) (M1)
Notes: Accept equivalent forms. Award (M1) for correct substitutions in mean formula.
OR
\(\frac{{48 + 2 \times {\text{ their part (a)}} + x}}{{11}}\) (M1)
10 (A1)(ft) (C2)
Note: Follow through from their answer to part (a).
