Friday

February 12, 2016
Posted by **KEENE** on Friday, February 6, 2009 at 7:38am.

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

- Statistics -
**Reiny**, Friday, February 6, 2009 at 9:15amabout 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

- Statistics -
**Anonymous**, Wednesday, October 21, 2009 at 9:24pmFor 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

- Statistics -
**Donna**, Sunday, August 14, 2011 at 6:24pmA 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.