I have a couple questions I answer for home work could some look atthem and tell me If I am doing them right I also am having problems understanding the variance and standard deviation are the site you can suggest that would help with this I need a step by step help

11. For the following scores, find the (a) mean,
Usually the best measure of central tendency is the ordinary average, the sum of all
the scores divided by the number of scores. In statistics, this is called the mean. The
average, or mean, of a group of scores is a representative value.
2+ 2 +0 + 5 + 1+ 4+ 1+ 3+ 0+ 0+ 1+ 4+ 4+ 0+ 1+ 4+ 3+ 4+ 2+ 1+ 0= 42
42/21=2

(b) median, Another alternative to the mean is the median. If you line up all the scores from
lowest to highest, the middle score is the median.

0 ,0,0,0,0, 1,1,1,1,1,2,2,2,3,3,4,4,4,4,4,5
Median 2

(c) sum of squared deviations,
0x0=0, 1x1=1, 2x2=4,3x3=9, 4x4=16, 5x5=25
0+0+0+0+0+1+1+1+1+1+4+4+4+9+9+16+16+16+16+16+25= 140

(d) variance

(e) standard deviation:

14.

On a standard measure of hearing ability, the mean is 300 and the standard deviation
is 20. Give the Z scores for persons who score
(a) 340

z=(340-300)/(20)

z=(40)/(20)

z=2

(b) 310

z=(310-300)/(20)

z=(10)/(20)

z=(1)/(2)

(c)260.

z=(260-300)/(20)

z=(-40)/(20)

z=-(40)/(20)

z=-2

Give the raw scores for persons whose Z scores on this test are
(d) 2.4

2.4*20+300=x

x=2.4*20+300

x=48+300

x=348

(e)1.5

1.5*20+300=x

x=1.5*20+300

x=30+300

x=330

(f) 0

0*20+300=x

x=0*20+300

x=0+300

x=300

(g) -4.5.

-4.5*20+300=x

x=-4.5*20+300

x=-90+300

x=210

any help would be appreciated
Thank you

about c)

the variance is the sum of the squares of the deviations from the mean.
Since most of you data values hover around 0-5, it is hard to tell whether you squared the differences or the actual data values.
I see a 5x5, so it appears that you simply squared the data values.

take each data value, subtract it from the mean, then square it.
now add these up, they should all be positive, and divide by 21
That is your variance.

the standard deviation is the square root of that variance.

I don't know at what level of sophistication your study of statistic is, but there is a difference in how the variance and standard deviations are calculated.
If you "google" variation and standard deviation, most pages will explain that difference
Here is a page that gives a short explanation

http://www.chem.utoronto.ca/coursenotes/analsci/StatsTutorial/MeasMeanVar.html

Your last question shows up as imcomplete.
A Z score is found by:
(your score - mean)/standard deviation

so suppose one of your values is 350, then the z-score for that data value would be (350 - 300)/20 or 2.5

For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:

3.0, 3.4, 2.6, 3.3, 3.5, 3.2

A psychologist interested in political behavior measured the square footage of the desks in the official office of four U.S. governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, and 36 square feet. (a) Figure the means and standard deviations for the governors and for the CEOs. (b) Explain, to a person who has never had a course in statistics, what you have done. (c) Note the ways in which the means and standard deviations differ, and speculate on the possible meaning of these differences, presuming that they are representative of U.S. governors and large corporations’ CEOs in general.

It looks like you have correctly calculated the mean and median for the given scores. Good job!

To calculate the variance and standard deviation, there are several steps involved. I'll explain them step by step:

1. Calculate the mean: You have already calculated it as 2.

2. Calculate the squared deviation for each score: To do this, subtract the mean from each score and square the result. For example, for the first score of 2, the squared deviation would be (2-2)^2 = 0. Do this for all the scores and sum them up.

3. Calculate the sum of squared deviations: You have correctly calculated it as 140.

4. Calculate the variance: The variance is the average of the squared deviations. To do this, divide the sum of squared deviations by the number of scores. In this case, divide 140 by 21 (number of scores). The result is the variance.

5. Calculate the standard deviation: The standard deviation is the square root of the variance. Take the square root of the variance calculated in step 4.

Now, for understanding variance and standard deviation in more detail, I recommend some online resources that provide step-by-step explanations:

Khan Academy's statistics course: Khan Academy offers a comprehensive course on statistics, including variance and standard deviation. It provides video tutorials and practice exercises to help you understand the concepts. You can access it at https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data.

Stat Trek's guide on variance and standard deviation: Stat Trek is a website that provides explanations of statistical concepts. They have a detailed guide on variance and standard deviation, including step-by-step formulas and calculations. You can check it out at https://stattrek.com/statistics/formulas.aspx.

I hope these resources help you in understanding variance and standard deviation better. If you have any more questions or need further assistance, feel free to ask!