2026 PHS P1 Q26

\((x-1)\quad(x+2)\quad(x-2)\quad(x+8)\quad(x-1)\quad(x+5)\quad(x+4)\quad(x+6)\)

The list shows the masses, in kg, of 8 parcels handled by delivery company \(A\).

The sum of the mode and the median of the masses is 36 kg.

1. Show that \(x=17\).[3]
2. Calculate the mean and standard deviation of the masses of the 8 parcels handled by delivery company \(A\).[2]
3. Delivery company \(B\) handled another 8 parcels.
   The mean mass of the parcels was 18 kg and the standard deviation was 3.12 kg.
   By commenting on the means and the standard deviations, compare the distributions of the parcel masses handled by delivery company \(A\) and \(B\).[2]