mean and standard deviation + check!

• May 31st 2007, 05:25 PM
bobbluecow
mean and standard deviation + check!
1) The mean and standard deviation of a set of data are two measurements that describe the data. A certain student has written 8 out 10 exams, which are equally weighed. The student misses the 9th exam and receives a score of 0. However, for the last exam, the student studied an incredible amount and scored 100% compare the mean and standard deviation after 8 unit test and after 10 unit test.
Both the mean and standard deviation are 50.

2) The following data in the sodium content (in milligrams) of 20 beef hotdogs:
495,477,425,322,482,587,370,322,479,375,330,300,38 6,401, 645, 440,317,319,298, 253
Determine the mean and standard deviation of the data:
Mean: 401.15
Standard deviation: 99.84

7) What is the mean and standard deviation?
Value:
4.8
5.2
5.4
5.9
6.5
6.6
Frequency:
25
21
23
17
24
25

Mean: 5.74
Standard deviation: 0.69

• Jun 2nd 2007, 10:24 AM
justin
I know 2 are right but not sure about the first one....
To be honest I can tell you that 2 and 7 are right: but I am not sure about question one maybe someone else can answer well good luck in your studies I am doing statistics and man is it ever confusing but mean and standard deviation are straight foward. well good luck!;)

2) The following data in the sodium content (in milligrams) of 20 beef hotdogs:
495,477,425,322,482,587,370,322,479,375,330,300,38 6,401, 645, 440,317,319,298, 253
Determine the mean and standard deviation of the data:
Mean: 401.15
Standard deviation: 99.84

correct good job:)

7) What is the mean and standard deviation?
Value:
4.8
5.2
5.4
5.9
6.5
6.6
Frequency:
25
21
23
17
24
25

Mean: 5.74
Standard deviation: 0.69 correct good job:)
• Jun 2nd 2007, 01:30 PM
CaptainBlack
Quote:

Originally Posted by bobbluecow
1) The mean and standard deviation of a set of data are two measurements that describe the data. A certain student has written 8 out 10 exams, which are equally weighed. The student misses the 9th exam and receives a score of 0. However, for the last exam, the student studied an incredible amount and scored 100% compare the mean and standard deviation after 8 unit test and after 10 unit test.
Both the mean and standard deviation are 50.

Let the sum of the marks on the first 8 exams be $\displaystyle S_8$ and the
sum of the squares of the marks be $\displaystyle SS_8$. Then the mean
of the first eight exams is:

$\displaystyle \mu_8 = S_8/8$

and the standard deviation is:

$\displaystyle \sigma_8 = \sqrt{(SS_8 - (S_8)^2)/8}$

Now the sum of all the exams $\displaystyle S_{10}=S_8 + 100$, and the sum of squares
$\displaystyle SS_{10}=SS_8 + 10000$. Then the final mean is:

$\displaystyle \mu_{10} = (S_8+100)/10 = (8\mu_8 + 100)/10$

and the standard deviation is:

$\displaystyle \sigma_{10} = \sqrt{(SS_{10} - (S_{10})^2)/10}$

Now this last needs to be rewitten in terms of $\displaystyle \mu_8$ and $\displaystyle \sigma_8$, which
is tedious but routine.

RonL