Question

The number of sweets in 25 bags has a mean of 30 and standard deviation of 3. In a special promotion, the manufacturer doubles the number of sweets in each bag. What do you think will happen to the mean and standard deviation. Calculate the new mean and standard deviation and state whether or not your guess was correct.

Answer 1

Answer:

Mean = 60

Standard Deviation = 6

Step-by-step explanation:

Number of bags = 25

Mean = x`= 30

Mean= Total number of sweets/ Total number of bags

30 = Total number of sweets/ 25

Total number of sweets= 30*25= 750

When the sweets are doubled then the number of sweets is 750 *2= 1500

Mean= Total number of sweets/ Total number of bags

Mean = 1500/ 25

Mean = 60 (twice the mean of 750 sweets = 30)

As x`= ∑x/n

But the new mean is calculated as

2x`= ∑( x.2)/n= 2. (30)= 60

The co efficient of Standard deviation is calculated as

Co efficient of SD = Standard Deviation/ Mean

= 3/30 = 0.1

Multiplying with the new mean would give

Co efficient of SD * Mean= Standard Deviation

60 *0.1 = 6

It is the property of the variance that when each observation is multiplied by the square of a constant ² the variance also increase by a² and so does the standard deviation.