Question

QUESTION THREE.
The following data give the savings bank accounts balances of nine sample
households selected in a survey. The figures are in SSP
745.2,000.1.500.68,000.461,549,3750,1800,4795
(a) Find the mean and the median for these data;
(6) Do these data contain an outlier? If so, exclude this value and recalculate th
mean and median. Which of these summary measures has a greater change wh
outlier is dropped?;
(c) Which of these two summary measures is more appropriate for this series?​

Answer 1

Answer:

We can first order the data from smallest value to largest value:

461

549

745

1500

1800

2000

3750

4795

68000

a) The mean is 9289, and the median is 1800

b) The data does have an outlier, which is 68000, because it is more that three standards deviations away from the mean, excluding this value, our new mean is 1950 and our new median is 1650. We can see that the greatest change in value was for the mean.

c) the median is more appropriate because the median is less sensitive to outliers. The mean can be easily swayed by outliers in either way, and this can give an erroneous impression of the data.