Advertisements
Advertisements
Question
The monthly incomes of 8 families in rupees in a certain locality are given below. Calculate the mean, the geometric mean and the harmonic mean and confirm that the relations among them holds true. Verify their relationships among averages.
| Family: | A | B | C | D | E | F | G | H |
| Income (Rs.): | 70 | 10 | 50 | 75 | 8 | 25 | 8 | 42 |
Advertisements
Solution
| Family | Income (₹) (x) |
log x | `1/"x"` |
| A | 70 | 1.8451 | 0.0143 |
| B | 10 | 1.000 | 0.1 |
| C | 50 | 1.6990 | 0.02 |
| D | 75 | 1.875 | 0.0133 |
| E | 8 | 0.9031 | 0.125 |
| F | 25 | 1.3979 | 0.04 |
| G | 8 | 0.9031 | 0.125 |
| H | 42 | 1.6232 | 0.0239 |
| 288 | 11.2465 | 0.4615 |
(i) Arithimetric Mean (AM) = `(sum "x")/"n" = 288/8` = 36
(ii) Geometric Mean (GM) = Antilog `((sum "log x")/"n")`
= Antilog `((11.2465)/8)`
= Antilog (1.4058)
= 25.46
(iii) Harmonic Mean (HM) = `"n"/(sum (1/"x"))`
= `8/0.4615`
= 17.33
Thus, 36 > 25.46 > 17.33
∴ AM > GM > HM
APPEARS IN
RELATED QUESTIONS
Find lower quartile, upper quartile, 7th decile, 5th decile and 60th percentile for the following frequency distribution.
| Wages | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |
| Frequency | 1 | 3 | 11 | 21 | 43 | 32 | 9 |
Calculate AM, GM and HM and also verify their relations among them for the following data.
| X | 5 | 15 | 10 | 30 | 25 | 20 | 35 | 40 |
| f | 18 | 16 | 20 | 21 | 22 | 13 | 12 | 16 |
The harmonic mean of the numbers 2, 3, 4 is:
The correct relationship among A.M., G.M. and H.M. is
Median is the same as:
The measure of central tendency that does not get affected by extreme values:
Which of the following best describes a 'measure of central tendency'?
Which type of average is defined as the value repeated the maximum number of times in a dataset?
The sum of deviations of all observations from the arithmetic mean of a dataset is always ______.
A frequency distribution has two classes with the highest and equal frequencies. What can be said about its mode?
