Rithvik's Blog GCSE

A group of detectives are investigating a series of mysterious disappearances in the town of Numeralia. They've gathered data on the ages of the 30 missing people, which are as follows: 15, 22, 19, 17, 34, 21, 18, 20, 16, 22, 25, 23, 18, 17, 19, 21, 20, 16, 15, 24, 20, 23, 25, 22, 17, 19, 21, 16, 15, 18. As a budding statistician, your task is to help the detectives by providing the following statistical insights: Calculate the mean, median, and mode of the ages. Determine the range of the data. Comment on what these statistics can tell us about the age group of the missing people. Provide your calculations and insights to assist the detectives in understanding if there's a pattern in the ages of the missing individuals.

A space probe travels along a path described by the function � ( � ) = � � 3 + � � 2 + � � + � f ( x ) = a x 3 + b x 2 + c x + d , where � a , � b , � c , and � d are constants. The probe starts its journey at � = 0 x = 0 and reaches its furthest point at � = 4 x = 4 hours, where it then changes its course. Given that the probe's path reaches a maximum height at � = 2 x = 2 hours and the heights at � = 0 x = 0 , � = 2 x = 2 , and � = 4 x = 4 are 0 0 , 64 64 , and 0 0 meters respectively, determine the values of � a , � b , � c , and � d . Hint: Use the conditions given to set up equations and solve for the unknowns.