Question 4 - A-Level Maths

Exam Board	Edexcel
Module	S1 (Statistics 1)
Year	2007
Session	January
Topic	Measures of Location and Spread
Type	Histogram from discrete rounded data

Summarised below are the distances, to the nearest mile, travelled to work by a random sample of 120 commuters.

For this distribution,

describe its shape,
use linear interpolation to estimate its median. The mid-point of each class was represented by $x$ and its corresponding frequency by $f$ giving $$\Sigma f x = 3550 \text { and } \Sigma f x ^ { 2 } = 138020$$
Estimate the mean and the standard deviation of this distribution. One coefficient of skewness is given by $$\frac { 3 ( \text { mean - median } ) } { \text { standard deviation } } .$$
Evaluate this coefficient for this distribution.
State whether or not the value of your coefficient is consistent with your description in part (a). Justify your answer.
State, with a reason, whether you should use the mean or the median to represent the data in this distribution.
State the circumstance under which it would not matter whether you used the mean or the median to represent a set of data.