What are the desiderata (requirements) of a good average? Compare the mean, the median and the mode in the light of these desiderata? Why averages are called measures of central tendency?

"Every average has its own peculiar characteristics. It is difficult to say which average is the " Explain with examples.

What do you understand .by 'Central Tendency'? Under what conditions is the median more suitable than other measures of central tendency?

The average monthly salary paid to all employees in a company was Rs 8,000.

The average monthly salaries paid to male and female employees of the company were Rs 10,600 and Rs 7,500 respectively. Find out the percentages of males and females employed by the company.

#### 1. Calculate the arithmetic mean from the following data:

Class               10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89

Frequency         2         4           9        11        12        6        4        2

#### 2. Calculate the mean, median and mode from the following data:

Height in Inches Number of Persons

 62-63 2 63-64 6 64-65 14 65-66 16 66-67 8 67-68 3 68-69 1 Total 50

A number of particular articles have been classified according to their weights.

After drying for two weeks, the same articles have again been weighed and similarly classified. It is known that the median weight in the first weighing was 20.83 gm while in the second weighing it was 17.35 gm.

Some frequencies a and b in the first weighing and x and y in the second are missing. It is known that a = 1/3x and b = 1/2 y. Find out the values of the missing frequencies.

 Class Frequencies First Weighing Second Weighing 0- 5 a z 5-10 b y 10-15 11 40 15-20 52 50 20-25 75 30 25-30 22 28
• Cities A, Band C are equidistant from each other. A motorist travels from A to B at 30 km/h; from B to C at 40 km/h and from C to A at 50 km/h. Determine his average speed for the entire

#### 3. Calculate the harmonic mean from the following data:

 Class-Interval 2-4 4-6 6-8 8-10 Frequency 20 40 30 10

A vehicle when climbing up a gradient, consumes petrol @ 8 km per

While coming down it runs 12 km per litre. Find its average consumption for to and fro travel between two places situated at the two ends of 25 Ian long gradient.