# Thread: mean and standard deviation + check!

1. ## 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

2. ## 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

3. 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