Question

The coefficients of variations for the two distributions are 60 and 70 and its standard deviations are 21 and 16 respectively. Determine its arithmetic mean

Answer 1

Given :-

The coffiecients of variations for the two distribution are 60 and 70 .

The standard deviation for 60 and 70 are 21 and 16 respectively.

Solution :-

Here, we have to calculate its arithmetic mean

For first distribution ,

We have ,

Coffiecients of variations = 60

Standard deviation = 21

Let the mean be x

As we know that,

Coffiecients of variations

= Standard deviation / mean * 100

Put the required values,

60 = 21 / x * 100

60x = 2100

x = 2100/60

x = 210/6

x = 35

Thus, The mean for first distribution is 35

Now,

For second distribution ,

We have,

Coffiecients of variations = 70

Standard deviations = 16

Let the mean be y

As we know that,

Coffiecients of variations

= Standard deviation / mean * 100

Put the required values,

70 = 16/y * 100

70y = 1600

y = 1600/70

y = 160/7

y = 22.85

Thus, The mean for second distribution is 22.85

Hence, The arithmetic mean is 35 and 22.85 $.$

Answer 2

Given :-

The coffiecients of variations for the two distribution are 60 and 70 .

The standard deviation for 60 and 70 are 21 and 16 respectively.

Solution :-

Here, we have to calculate its arithmetic mean

For first distribution ,

We have ,

Coffiecients of variations = 60

Standard deviation = 21

Let the mean be x

As we know that,

Coffiecients of variations

= Standard deviation / mean * 100

Put the required values,

60 = 21 / x * 100

60x = 2100

x = 2100/60

x = 210/6

x = 35

Thus, The mean for first distribution is 35

Now,

For second distribution ,

We have,

Coffiecients of variations = 70

Standard deviations = 16

Let the mean be y

As we know that,

Coffiecients of variations

= Standard deviation / mean * 100

Put the required values,

70 = 16/y * 100

70y = 1600

y = 1600/70

y = 160/7

y = 22.85

Thus, The mean for second distribution is 22.85

Hence, The arithmetic mean is 35 and 22.85 ..