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S1 solomon paper question

An adult evening class has 14 students. The ages of these students have a mean of 31.2 years and a standard deviation of 7.4 years.
A new student who is exactly 42 years old joins the class. Calculate the mean and standard deviation of the 15 students now in the group.

Can someone explain how to do this question step-by-step please? My teacher didn't explain coding very well and I can't find any videos on it so i'm a little bit stuck....
I think I know how to do the mean- you could solve it algebraically somehow? Meh
Original post by jessyjellytot14
An adult evening class has 14 students. The ages of these students have a mean of 31.2 years and a standard deviation of 7.4 years.
A new student who is exactly 42 years old joins the class. Calculate the mean and standard deviation of the 15 students now in the group.

Can someone explain how to do this question step-by-step please? My teacher didn't explain coding very well and I can't find any videos on it so i'm a little bit stuck....
I think I know how to do the mean- you could solve it algebraically somehow? Meh


It's nothing to do with coding.

You just need to use the formulae for the mean and s.d.

I'll outline the mean:

Mean is 31.2 yrs.
So, total number of years for 14 students is...?
Add extra student with 42 years.
New mean for 15 students is...?
Original post by ghostwalker
It's nothing to do with coding.

You just need to use the formulae for the mean and s.d.

I'll outline the mean:

Mean is 31.2 yrs.
So, total number of years for 14 students is...?
Add extra student with 42 years.
New mean for 15 students is...?


Could you please point out how to start the working out for standard deviation? :colondollar:
Reply 3
Avatar for Zacken
Zacken
22
Original post by Namita Gurung
Could you please point out how to start the working out for standard deviation? :colondollar:


Outline for standard deviation:

1) find the variance.

2) using the old mean, find an expression for sum of squares of years.

3) add the value of 42^2 and then re-calculate the variance.

4) square root.
Original post by ghostwalker
It's nothing to do with coding.

You just need to use the formulae for the mean and s.d.

I'll outline the mean:

Mean is 31.2 yrs.
So, total number of years for 14 students is...?
Add extra student with 42 years.
New mean for 15 students is...?


Would this be 31.2 x 14 = 436.8?
And then add 42 and divide by 15?
Reply 5
Avatar for Zacken
Zacken
22
Original post by jessyjellytot14
Would this be 31.2 x 14 = 436.8?
And then add 42 and divide by 15?


Yeah.
mean=sum of ages/number of students
31.2=sum of ages/14
sum of ages=436.8
Now plug it back into the equation to find the mean:
436.8+42/15=32.92 which is the new mean.
Now for SD:
original variance=sum of ages^2/14 -31.2^2
sum of ages^2= (7.4^2 + 31.2^2)*14
sum of ages^2=14394.8
New variance= (14394.8+42^2)/15 - [(436.8+42)/15]^2
new variance= 58.3669333......
new SD=7.639825478
Reply 7
Avatar for Zacken
Zacken
22
Original post by Dominator1
...


Full solutions are against forum guidelines.
Original post by Zacken
Outline for standard deviation:

x
.


Thank you! :hugs:
I don't know why it took me so long to get it. :ashamed2:

Original post by Zacken
Full solutions are against forum guidelines.


woops - deleted mine now. ty

Original post by Dominator1
x



I got that as well :woo:
(edited 7 years ago)
Original post by Zacken
Outline for standard deviation:

1) find the variance.

2) using the old mean, find an expression for sum of squares of years.

3) add the value of 42^2 and then re-calculate the variance.

4) square root.


What do you mean by this?
Reply 10
Avatar for Zacken
Zacken
22
Original post by jessyjellytot14
What do you mean by this?


What's the formula for variance?
Original post by Zacken
What's the formula for variance?


Sum of fx2/n minus the mean squared ?
Original post by jessyjellytot14
Sum of fx2/n minus the mean squared ?


That would be for a frequency distribution. For raw data we have:

Var=∑x2n−xˉ2\displaystyle Var=\frac{\sum x^2}{n}-\bar{x}^2

Since this equals 7.427.4^2, you've got sufficient information to work out the sum of the squares.

And proceed as Zacken suggested.
Reply 13
Avatar for Emariya
Emariya
3
Thank you so much..👍😃

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