COM3710 - Section 1 - Homework 1




riosjosh

Comm 3710 Homework 1 (10 points possible, Due 9-13)
  1. Define the following terms and symbols. If a formula is presented provide a clear definition of the formula. If a term is presented, provide a definition and a computational formula. Two examples are provided below.
    1. [SUM]X2 = To solve this, I would first square each score, then sum the squared scores.
    2. ([SUM]X)2 = To solve this, I would first sum the scores, then square the sum
    3. [SUM]X/N = To solve this, I would first sum the scores, then divide the sum by the number of scores
    4. mean = the sum of each score divided by the number of scores
    5. variation = is the sum of the squares; SS=[SUM]X2 – ([SUM]X)2/N
    6. variance = is the average dispersion; S2=SS/N=([SUM]X2 – ([SUM]X)2/N)/N
    7. standard deviation = is the square root of the variance; S=[ROOT]S2=[ROOT](SS/N)=[ROOT]([SUM]X2 – ([SUM]X)2/N)/N
    8. median = This is the middle point of the data when lined up in order
    9. [SUM] (X-Xbar)2 = this is the conceptual formula for variation
    10. s=[ROOT]S2=[ROOT](SS/N)=[ROOT]([SUM]X2 – ([SUM]X)2/N)/N; this is the standard deviation
    11. s2=SS/N=([SUM]X2 – ([SUM]X)2/N)/N; this is the variance
    12. SS=[SUM]X2 – ([SUM]X)2/N; sum of squares; this is the variation
  2. For this problem use the dataset “Homework One Data Set Fall 2011”. Use Excel to calculate X2, the sum of X, and the sum of X2. Print out the sheet and calculate the mean, median, mode, variation, variance, and standard deviation for the X variable. Use the computational formulas, print your hand calculation on the excel sheet, and CIRCLE your final answer.



N
X
X2
1
19
361
2
21
441
3
22
484
4
24
576
5
25
625
6
26
676
7
30
900
8
31
961
9
37
1369
10
38
1444
11
41
1681
12
46
2116
Sum =
360
11634

Variation
834

SS=∑X^2 – (∑X)^(2)/N = 11634 - (360)^(2)/12 = 11634 - 129600/12 = 11634 - 10800 = 834
Variance
69.5

S^2 = SS/N = (∑X^2 – (∑X)^2/N)/N = (11634 - 360^(2)/12)/12 = (11634 - 129600/12)/12 = (11634 - 10800)/12 = 834/12 = 69.5
Standard

Deviation
8.34

S=√S2=√(SS/N)=√((∑X2 – (∑X)2/N)/N) =√((11634 - 360^(2)/12)/12) = √((11634 - 129600/12)/12) = √((11634 - 10800)/12) = √(834/12) = √(69.5) = 8.34

Mean
30

=(19+21+22+24+25+26+30+31+37+38+41+46)/12 = 360/12 = 30
Median
28


Mode
None






  1. If the mean of a dataset is 17.28, and you add 10 points to every score in the dataset, what would be the value of the new mean in the new data set?

The new mean in the new data set will be 27.28. This is found by adding the constant 10 to the old mean 17.28. 17.28+10=27.28

  1. If the standard deviation of a data is 8, and you multiplied every score in dataset by 2, what would be the standard deviation of this new set of scores?

The standard deviation is multiplied by the constant. So the standard deviation would be 16.

  1. If the variance of a set of scores is 81, what is the standard deviation?

Then the standard deviation is 9. S=[ROOT](S2) or S=[ROOT](variance) so S=[ROOT]81 then S=9