PSYC 2021
OPTIONAL ASSIGNMENT #1 Feedback
A. BASIC MATH(order of priority, fractions) In case of doubt consult Khanacademy.org
1.5 + 22 – 3 x 2 = 5 + 4 – 6 =36.½ + ¾= 2/4 + ¾ = 5/4 or 1.25
2.(5 + 2)2 – 3 /2 = 72 – 1.5 =47.57.2/3 + 4/5 = 10/15 + 12/15 = 22/15
3.(3 – 5)2 + √9 x 4= (-2)2+3x4=4+12=168.2/3 x 4/5 = (2 x 4)/(3 x 5) = 8/15
4.2 + √4 + 3 x 5 = 2 + 2 + 15 = 199.2/3 : 4/5 = (2 x 5)/(3 x 4) = 10/12
5.7 – 4/2 + 6 x-32 =7–2+6x9= 5+54 = 5910.(2+4)/(4+5)= 6/9 = 2/3
Re 5: It could be argued that -32= +9 only if in parentheses (-3)2. In that case -49 O.K.
B. SCALES OF MEASUREMENT: In case of doubt, review the characteristics of the various scales
For the variables below, indicate on which type of scale it is measured:
1. Social insurance numbersNominal
2.Letter grades received on an exami = 5 shifts to i=10 above AOrdinal
F(<40)E(40-49) D(50-54) D+(55-59)... B+(75-79) A(80-89)...
3.Overall ranking of products Ordinal
4.Grade point (F=0, E=1,D=2,D+=3 ...A=8, A+=9)Ratio
5.Amount of Money in the bankRatio
6.Weight measured in kgRatio
7.Intelligence quotient (IQ)Interval
8.AgeRatio
9.Order of arrival in a raceOrdinal
10.Product codes on the grocery shelfNominal
Difficulties experienced on this set of questions seems to indicate not lack of mental ability (because very little is needed) but rather lack of mental fitness, i.e. a tendency to passively rely on memory and guesses rather than actively asking oneself pertinent questions aboutthe variable. E.g. age was said by some to be measured on a nominal scale, others considered it an ordinal scale, still others thought it was a mere interval scale.Can a person’s age really be no more than a label? Is 40 years more than 20 years? If yes, the variable must be at least measured an ordinal scale. Is the distance between 20 years and 21 years the same as the distance between 21 and 22 and all other successive years? If yes, the variable is at least of an interval scale. Is 40 years twice as old as 20 years? If yes, it must be a ratio scale.
NOTE: lack of mental fitness is a predictor of trouble getting through this course.
C. UNIT OF MEASUREMENT (discontinuous vs. continuous scales)
For each of the variables below, indicate whether it is discontinuous, genuinely continuous or approximates continuity (i.e. practically continuous since unit is very small relative to range).
1.height of a growing plant or person as it is naturally changingContinuous
2.height of a growing plant measured in cmDiscontinuous
3.change in temperature as it is naturally occurringContinuous
4.change in temperature as measured in CelsiusDiscontinuous
5.Income per month of employees within a companyDiscontinuous
6.average income of employees within a companyContinuous
7.number of grains of sand as seen through a strong microscopeDiscontinuous
8.amount of sand seen on a beach with the naked eyeContinuous
NOTE: If this set of questions gave you trouble, there is no need to worry about it too much
D 1.Calculate the following measures for each of the sets of numbers listed below:
mean / median / mode / ∑X / ∑X2 / (∑X)2/N / SS / s2 / s / IQR / Rangea / 3.25 / 3 / 2 / 39 / 293 / 126.75 / 166.25 / 13.85 / 3.72 / 6.5–0.5 = 6 / 9-(-3) +1=13
b / 4.58 / 5.5 / 6 / 55 / 373 / 252.08 / 140.92 / 11.74 / 3.43 / 6.5–0.5= 3 / 9-(-4) +1=14
c / 9.58 / 10.5 / 11 / 115 / 1243 / 1102.08 / 140.92 / 11.74 / 3.43 / 11.5-8.5 =3 / 14-1 +1 = 14
d / -0.42 / 0.5 / 1 / -5 / 143 / 2.08 / 140.92 / 11.74 / 3.43 / 1.5 - -1.5=3 / 4 –(-9)+1=14
e / 1.58 / 2.5 / 3 / 19 / 171 / 30.08 / 140.92 / 11.74 / 3.43 / 3.5 – 0.5=3 / 6 –(-7)+1=14
f / 1.42 / 5.5 / -7 +7 / 17 / 663 / 24.08 / 638.92 / 53.24 / 7.30 / 7.5- -6.5=14 / 10+10+1=21
g / 5.92 / 6 / 10 / 71 / 565 / 420.08 / 144.92 / 12.08 / 3.47 / 9.5 – 3 = 6.5 / 10 – 0+1 =11
h / 0 / 0 / 0 / 0 / 70 / 0 / 70 / 5.83 / 2.42 / 1.5 - -1.5=3 / 4 -(-5)+1 =10
The values of strings b, c, d, and e only differ by a constant. Note that their SS and their various measures of dispersions are identical. Median, IQR, Range, and Mode are easily determined if one puts the values in order. Problems result from taking short-cuts.
NOTE that being sloppy and taking short-cuts rather than proceeding in a systematic fashion is a predictor of trouble to come, so is the inability to calculate SS.
Q1 Q2 Q3
a.-3-20 |122 |456 |789
b.-4 03 |455 |666 |789
c.158 |91010 |111111 |121314
d.-9-5-2 |-100 |111 |234
e.-7-30 |122 |333 |456
f.-10-7-7 |-6-55 |677 |8910
g.012 |455 |789 |101010
h.-5-3-2 |-100 |011 |234
2.Which measure of central tendency and measure of dispersion are most appropriate for each of the above sets of data?
a / b / c / d / e / f / g / hCentral
Tendency / Mean if one wants to have the most precise measure
or median if one wants to have a fast measure / Modes / Mean or median / Any of the three
Measure Dispersion / Standard deviation if calculating the mean
or IQR to accompany the median / Range / S or IQR / Range
Why? / Mean and median are quite similar and both of these measures of central tendency represent the data / Mean& median
not informative / little difference / Most in-formation
E. USE OF THE NORMAL CURVE
IQ scores distribute normally with a mean of µ = 100 and a standard deviation of σ=15.
For each question make yourself a sketch to indicate what you are looking for.
1.Which percentile corresponds to an IQ of 115?P84
2.What is the probability of encountering an IQ that is equal or below 95 (≤ 95)?p = .37
3.What is the probability of finding an IQ that is equal or above 95 (≥95)?p = .63
4. What is the probability of an IQ score between 80 and 120?p = .82
5.An employer wants to hire people who are smart but not too smart.
If N=200 randomly selected people apply, how many will fall between 90 and 120? f = p x N = 131
6.The employer wants people with IQs between 110 and 120. How many are there? f = 16
7.A school board wants to introduce classes for children with IQs between 70 and 80
What is the probability of such IQ scores? p =.07
How many will there be among 2,000? f = p x N = .07x2,000f = .07x2000f = 138