The mean and standard deviation of a group of 20 boys height's are 165 cm and 6.1 cm respectively. If a boy who is 1.76m leaves the group find the new mean and variance of a sample of 62 people.

Question

campbell_st · Answer

well you set up an equation 

Mean = sum of the score/number of scores

so 165 = sum of scores/ 20

so the total for the sum of the scores is 165 * 20 

then is 1.76 tall person leaves... subtract 176 from the total

so the new mean will be 

Mean = (165 * 20 - 176)(19)

I hope this makes sense...

campbell_st · Answer

the sum of the deviations will be change as (176- 165) is removed from the data...

so using the standard deviation fromula 

$$SD = \sqrt{\frac{1}{n} \sum_{n}^{i = 1}(x_{i} - \mu)^2}$$ 

so 

$$6.1 = \sqrt{\frac{1}{20}\sum_{x_{i} = 1}^{20}(x_{i} - 165)^2}$$

then 

$$6.1 ^2 \times 20 = \sum_{i = 1}^{20} (x_{i} - 165)^2$$

so $$\sum_{i=1}^{20} (x_{i} - 165)^2 = 744.2$$

so you need to subtract (176 - 165)^2 to find the new total of the deviations squared. 

so the sum of the deviations is 623.2

then 

$$SD = \sqrt{\frac{1}{19} \times 623.2}$$

hope this helps... you just need to finish the calculations.