Question

Mean and standard deviation of two
distributions of 100 and 150 items are 50,
5 and 40, 6 respectively. Find the mean and
standard deviations of all the 250 items taken
together.​

Answer 1

Step-by-step explanation:

A)

 

Mean x¯=∑xinx¯=∑xin

Given x¯=50x¯=50

n=100n=100

50=∑xi10050=∑xi100

=50×100=50×100

=5000=5000

Sum of all the item= 5000

Step 2:

Standard deviation σ=∑x2in−(∑xin)2−−−−−−−−−−−−−−−√σ=∑xi2n−(∑xin)2

σ2=∑x2in−(∑x2in)2σ2=∑xi2n−(∑xi2n)2

Given σ=4,n=100,mean=50σ=4,n=100,mean=50

42=∑x2i10042=∑xi2100−502−502

16+2500=∑x2i100

Answer 2

Answer:

mean of all 25 items  = 44

standard deviation of all 250 items  = 5.6

Step-by-step explanation:

i.)$n_1$ = 100

ii.) $n_{2}$ = 150

iii) mean = $\frac{100\times 50 + 150\times40}{100 + 150} = \frac{5000 + 6000}{250} = \frac{11000}{250} = 44$

iv) standard deviation = $\sqrt{\frac{\{(100-1)\times(5)^2\} + \{(150-1)\times(6)^2\} }{250} } = 5.6$