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Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge
Edition 6ISBN: 130527010XIntroductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge
Edition 6ISBN: 130527010XThe following table contains monthly housing expenditures for 10 families.
Family | Monthly Housing Expenditures (Dollars) |
1 | 300 |
2 | 440 |
3 | 350 |
4 | 1,100 |
5 | 640 |
6 | 480 |
7 | 450 |
8 | 700 |
9 | 670 |
10 | 530 |
(i) Find the average monthly housing expenditure.
(ii) Find the median monthly housing expenditure.
(iii) If monthly housing expenditures were measured in hundreds of dollars, rather than in dollars, what would be the average and median expenditures?
(iv) Suppose that family number 8 increases its monthly housing expenditure to $900 dollars, but the expenditures of all other families remain the same. Compute the average and median housing expenditures.
Verified
Step 1 of 5
The following table shows the monthly housing expenditure of different families:
| Family | Monthly expenditure |
| 1 | 300 |
| 2 | 440 |
| 3 | 350 |
| 4 | 1100 |
| 5 | 640 |
| 6 | 480 |
| 7 | 450 |
| 8 | 700 |
| 9 | 670 |
| 10 | 530 |
Step 2 of 5
(i)
The average monthly housing expenditure can be found by adding all the expenditures and dividing it by number of family (10) as written below:
The average monthly housing expenditure is
.
Step 3 of 5
(ii)
Median is the middle value of a series. To find out median, first arrange the series in ascending order. Median is equal to
divided by 2. Here n is the number of observations. The re-arranged series of monthly income would be as written below:
The median is calculated below:
The 5th and 6th terms in the arranged data set are 480 and 530. The median therefore is the average of both terms:
The median monthly housing expenditure is
.
Step 4 of 5
(iii)
If the monthly housing expenditures had been measured in hundreds of dollars, the mean and median both would change. This is so because each observation will be in hundreds of dollars which would lead to the value of mean and median also in hundreds of dollars. The median would still be 5.5th term (as explained in part (ii) due to non-change in number of observations). Thus, the mean would be
and median would be
.
Step 5 of 5
(iv)
If the income of family 8 increases to $900, the mean would change. However, the median would remain the same due to no change in the number of observations. Mean is known to be affected by extreme values. The new mean would be as calculated below:
Thus, the new mean is
and the median is the same, that is, 
.
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