Chapter 13
4, 7, 8, 9, 10, 12, 13, 17 2. 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 Find the mean deviation about the median for the data in Exercises 3 and 4.
13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17 4. 36, 72, 46, 42, 60, 45, 53, 46, 51, 49 Find the mean deviation about the mean for the data in Exercises 5 and 6.
| x | i | 5 | 10 | 15 | 20 | 25 |
|---|---|---|---|---|---|---|
| f | i | 7 | 4 |
6 3 5
| x | i | 10 | 30 | 50 | 70 | 90 |
|---|---|---|---|---|---|---|
| f | i | 4 | 24 | 28 | 16 | 8 |
Find the mean deviation about the median for the data in Exercises 7 and 8.
| x | i | 5 | 7 | 9 | 10 |
|---|
12 15
| f | i | 8 | 6 | 2 |
|---|
2 2 6
| x | i | 15 | 21 | 27 | 30 | 35 |
|---|---|---|---|---|---|---|
| f | i | 3 | 5 | 6 | 7 | 8 |
Find the mean deviation about the mean for the data in Exercises 9 and 10.
Income per0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 day in `
| Number | 4 | 8 | 9 | 10 | 7 | 5 | 4 | 3 |
|---|
of persons
Height 95-105 105-115 115-125 125-135 135-145 145-155 in cms
| Number of | 9 | 13 | 26 |
|---|
30 12 10 boys
Find the mean deviation about median for the following data : Marks 0-10 10-20 20-30 30-40 40-50 50-60 Number of 6 8 14 16 4 2 Girls
| Calculate the mean deviation about median age for the age distribution of | 100 |
|---|
persons given below: Age 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 (in years)
| Number | 5 | 6 | 12 | 14 | 26 | 12 | 16 | 9 |
|---|
[Hint Convert the given data into continuous frequency distribution by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval] 13.4.3 Limitations of mean deviation In a series, where the degree of variability is very high, the median is not a representative central tendency. Thus, the mean deviation about median calculated for such series can not be fully relied. The sum of the deviations from the mean (minus signs ignored) is more than the sum of the deviations from median. Therefore, the mean deviation about the mean is not very scientific.Thus, in many cases, mean deviation may give unsatisfactory results. Also mean deviation is calculated on the basis of absolute values of the deviations and therefore, cannot be subjected to further algebraic treatment. This implies that we must have some other measure of dispersion. Standard deviation is such a measure of dispersion.