2.02h Recognize outliers

A survey was conducted into the annual salary offered for 19 different jobs in 2008. The results were as follows, in thousands of pounds.

15	16	18	19	21	36	36	38	41	41
43	47	51	55	56	60	62	64	110

It was decided to undertake a further study to see if self-esteem was correlated with level of annual salary. A random sample of 11 employees was taken and self-esteem was rated on a scale of 1 to 10 with the highest self-esteem being 10. The results were as follows.

Salary in £10 000's	1	2	3	4	5	6	7	8	9	10	11
Self-esteem	4	3	5	1	7	7	8	5	10	7	9

The table summarises 43 birth weights as recorded for babies born in a particular hospital during one week.

Birth weight (w kg)	\(2.0 \leqslant w < 2.5\)	\(2.5 \leqslant w < 3.0\)	\(3.0 \leqslant w < 3.5\)	\(3.5 \leqslant w < 4.0\)	\(4.0 \leqslant w < 4.5\)
Frequency	1	6	9	17	10

1. State the type of skewness of the data. [1]
2. Given that the lower quartile is 3.21 kg and the upper quartile is 3.96 kg, determine whether there are any babies whose birth weights might be regarded as outliers. [4]
3. The mean birth weight was found to be 3.58 kg. However, it was discovered subsequently that the table includes the birth weight, 2.52 kg, of one baby that has been recorded twice. Find the mean birth weight after this error has been removed. [3]

The table shows fuel economy figures in miles per gallon (mpg) for some new cars.

Car	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O
Mpg	57	40	34	33	11	17	30	27	31	20	35	24	26	23	32

1. Find the median and quartiles for the mpg of these 15 cars. [2]
2. Use the values in part (a) to identify any cars for which the mpg is an outlier. [3]

The table shows fuel economy figures in miles per gallon (mpg) for some new cars.

1. Find the median and quartiles for the mpg of these 15 cars. [2]
2. Use the values in part (a) to identify any cars for which the mpg is an outlier. [3]