Respuesta :
The mean age is 34.2. I'm working on the standard deviation right now, I'll comment on this post when I figure it out.
Answer:
A. The mean age of the ten people at a party is: Â 34.2
B. The standard deviation is: 10.3066
Step-by-step explanation:
We are given a information about the age of ten people as:
    Age(in years)        Number of people
       30                  5
       32                  3
        31                  1
        65                  1
Hence, the mean of the age is calculated as:
[tex]Mean(x')=\dfrac{30\times 5+32\times 2+31+65}{10}\\\\\\Mean(x')=\dfrac{342}{10}\\\\\\Mean(x')=34.2[/tex]
Now, we calculate the standard deviation in the following steps:
      x       x-x'      (x-x')²
     30      -4.2      17.64
     30      -4.2      17.64 Â
     30      -4.2      17.64
     30      -4.2      17.64
     30      -4.2      17.64
      32     -2.2       5.06
      32     -2.2       5.06
      32     -2.2       5.06
      31      -3.2      10.24
      65      30.8      948.64
∑ (x-x')²=  1062.26
Variance=∑ (x-x')²/10=106.226
Hence, standard deviation is the square root of variance.
standard deviation is:
[tex]=\sqrt{106.226}=10.3066[/tex]
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