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Homework 02 - Answers and Points

# Homework 02 - Answers and Points -  ...

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Unformatted text preview:   Homework Assignment 2          Psychology 60  Spring 2010  1. (4 points total)  Use summation notation to express each of the following calculations:  a. (1 point) Square each score, then add the squared values.  ΣXi2 or Σ( Xi2 ) or ΣX 2 or Σ( X 2 )   b. (1 point) Add the scores, then square the sum.  ( ΣXi )2 or ( ΣX )2   c. (1 point) Add two points to each score, then add the resulting values.  Σ( Xi + 2 ) or Σ( X + 2 )   d. (1 point) Add the scores, then subtract 6 points from the total.  ( ΣXi ) − 6 or ( ΣX ) − 6 or ΣXi − 6 or ΣX − 6     2. (3 points) Construct a grouped frequency distribution table to organize the following set of  scores, which range from 88 to 470.  319,   241,   104,  165,   97,   452,   280,    88,  225,  396,  271,  233,  470,  356,  159,  266,  112,  293,  174,  268,  153       X    f    450­499  2    400­449  0    350­399  2            note: several ways to do this. Full points if there are     300­349  1   about 10 classes of equal spacing without any bins     250­299  5   omitted    200­249  3    150­199  4    100­149  2  50­99    2    3. (3 points) Line charts are sometimes used incorrectly to display data that should be  presented in a bar chart. For example, the following line chart is an incorrect way to show  the average GPA in five different majors at UCSD. Explain in your own words why a line chart  is inappropriate for data such as these.      For these data it is inappropriate to use a line chart. Line charts  should not be used when the x axis is nominally scaled. The  reason is that using a line chart here implies that there is some  sensible point between the categories on the x axis. Because the  categories on the x axis are college majors (a nominal scale) and  they’re not ordered in some way that represents an underlying  continuous scale, it is not appropriate to have a line connecting  the categories.  A bar graph is the appropriate chart.      4. (3 points) Come up with a hypothetical data example in which the use of a scatter plot  would be a correct way to visualize data. You do not need to produce hypothetical data, only  a situation and the names of the variables you would measure.   For full credit the answer must have two variables that are both measured on  an interval or ratio scale and can be measured from the same unit.  For  example, individuals’ heights and weights. Both of these variables are ratio  scale, and both can be obtained from the same individual.     5.  (3 points) Sketch a histogram showing the distribution of scores presented in the following  table:      X  5  4  3  2  1              f  1  5  6  3  2    6. (3 points) An instructor at the state college recorded the academic major for each student in  a psychology class. Construct a frequency distribution table for the following results:                  Psych    Heath    Soc    Hist    Nurs        Bio    Phys Ed  Health   Psych    Soc                          Soc  Psych    Psych    Art    Psych    Engl    Art    Phys Ed  Health   Psych    Psych  Psych  Soc  Psych  Pol Sci   X    f  _______________________  ART    2  BIO    1  ENGL    1  HEALTH  3  HIST    1  NURS    1  PHYS ED  2  POL SCI  1  PSYCH  9  SOC    4    Other orders are fine, as well.             7. (2 points) A population of N = 25 scores has a mean, μ = 10.  What is the value of ∑Xi for this  population?    ΣXi ΣXi µ= , 10 = , ∴ ΣXi = 250          (note ∴ means “therefore”)  N 25   8. (4 points total) Does it ever seem to you that the weather is nice during the work week, but  lousy on the weekend?  Cerveny and Balling (1988) have confirmed that this is not your  imagination – pollution accumulating during the work week most likely spoils the weekend  weather for people on the Atlantic coast.  Consider the following hypothetical data showing  the daily amount of rainfall for 10 weeks during the summer.  Week  Av. Daily Rainfall  Weekdays (M – F)  Av. Daily Rainfall  Weekends (Sat. / Sun.)  1  1.2  1.5  2  0.6  2.0  3  0.0  1.8  4  1.6  1.5  5  2.4  0.2  0.8  8  0.9  1.6  9  1.1  1.2  10      2.1  7    2.2  6    0.8  1.4  1.7    a. (3 points, ‐‐ 1.5 for each mean‐‐) Calculate the average daily rainfall (the mean) during  the week, and the average daily rainfall for the weekends.    ΣXi 9.9 Xweek = , Xweek = , ∴ Xweek = 0.99   n 10   ΣXi 16.7 Xweekend = , Xweekend = , ∴ Xweekend = 1.67   n 10 b. (1 point) Based on the two means, does there appear to be a pattern in the data?  Yes, there is a mean difference between these samples; it rained more on the  weekends sampled than the weekdays sampled.     (note: need to do more work before we can conclude that this is good evidence  for a true difference rather than just sampling error)     9. (3 points –1 for each measure of central tendency‐‐) Find mean, median, and mode for the  following sample of scores:  7, 5, 9, 7, 7, 8, 6, 8, 10, 7, 4, 6  ΣXi 84 , X= , ∴ X = 7  n 12     Mean:  X =       Median:   Step 1 (Order scores): 4, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 10   Step 2 (find middle two scores, N/2, N/2 +1):   7, 7  Step 3 (find mean of middle two scores): (7+7) / 2 =7  Median = 7        Mode (most common score): 7  ...
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