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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?​

User Penguru
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2 Answers

3 votes

Final answer:

The initial data set's mean was 10066.67 SSP, and the median was 1800 SSP. After removing the outlier (68000), the new mean was 2825 SSP, and the median remained the same at 1800 SSP. The median is considered more appropriate as a measure for this data set because it is less influenced by the extreme outlier.

Step-by-step explanation:

a) To find the mean of the given data, we add all the data values together and divide by the number of data values.

The given data values in SSP are: 745, 2000, 1500, 68000, 461, 549, 3750, 1800, 4795.

Their sum is 745 + 2000 + 1500 + 68000 + 461 + 549 + 3750 + 1800 + 4795 = 90600.

Since there are 9 households, we divide 90600 by 9 to get the mean, which is 90600 / 9 = 10066.67 SSP.

To find the median, we arrange the data values in ascending order and locate the middle value. If there is an even number of data values, we take the average of the two middle values. The ordered data values are: 461, 549, 745, 1500, 1800, 2000, 3750, 4795, 68000.

The middle value is 1800, hence the median is 1800 SSP.

b) It seems that the value 68000 is an outlier, as it is much larger than the rest of the data. Excluding this value, we get the new sum as 90600 - 68000 = 22600.

The new mean with the outlier removed is 22600 / 8 = 2825 SSP, and the new median without the outlier (since 68000 was the last value) remains 1800 SSP.

Both the mean and median changed, but the mean changed more significantly when the outlier was dropped, indicating that the mean is more sensitive to outliers.

c) For this series, considering the presence of an outlier, the median is more appropriate as a measure of central tendency because it is less affected by extreme values.

User Sachin Rasane
by
7.2k points
4 votes

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.

User Gbero
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6.3k points