Module 4 Stats Questions and answers
What term refers to a frequency distribution that follows a bell-shaped, symmetrical, and unimodal
curve? ✅✅normal distribution
In a normal distribution, the mean is located where? ✅✅in the middle of the curve
T/F For a normal curve, the median, mean, and mode are typically equal
T/F The area below the curve is 120%. ✅✅True
False. 100% or 1.00
T/F The greater the standard deviation, the less spread out the normal curve. ✅✅FALSE
The greater the standard deviation, the more spread out the normal curve. The smaller the standard
deviation, the narrower the normal curve.
A normal distribution can be defined by its ___ and ______. ✅✅mean and standard deviation
the ___-___-___ rule
con? ✅✅68-95-99.7
However, the rule only works when values are exactly 1, 2, or 3 standard deviations away from the
mean. In order to apply the concept of proportions to other standard deviation values, such as σ = ±
1.4 or σ = ± 2.3, scores or values in the dataset must be standardized.
an exact value that is observed ✅✅raw score
, indicates exactly how many standard deviations a raw score is above or below the mean.
✅✅standard score
describes the exact location of a raw score within the whole distribution when compared to the
mean. It converts each raw score X into a signed, numerical value.
also known as standard scores ✅✅z-score
What does a +z-score mean?
what does a -z-score mean? ✅✅the value from the dataset lies above the mean
the value from the dataset lies below the mean
Coverting raw scores to z-scores ✅✅z= (raw score- mean)/ standard deviation
Converting z-scores to raw scores ✅✅raw score= mean + z * standard deviation
Comparing Values using z-Scores and Raw Scores
When comparing z-scores from the same population or sample, it may be more meaningful to
convert the z-score back to a raw score. For example, compare the performances of the following
students on the physiology exam (μ = 87 , σ = 4 ) given the -scores listed below for Josef, Marco, and
Brooklyn.
Josef: z=-1.75
Marco: z=-2.50
Brooklyn: z=1.25 ✅✅Convert each z-score to a raw score. Then compare the raw scores.
Josef: X=87 - 1.75(4) = 80
Marco: X= 87 - 2.50(4) = 77
Brooklyn: X= 87 + 1.25(4) = 92
z-Scores for Sample Means from a Population ✅✅(sample mean-population mean)/ population
mean/ sqrt(sample size)
What term refers to a frequency distribution that follows a bell-shaped, symmetrical, and unimodal
curve? ✅✅normal distribution
In a normal distribution, the mean is located where? ✅✅in the middle of the curve
T/F For a normal curve, the median, mean, and mode are typically equal
T/F The area below the curve is 120%. ✅✅True
False. 100% or 1.00
T/F The greater the standard deviation, the less spread out the normal curve. ✅✅FALSE
The greater the standard deviation, the more spread out the normal curve. The smaller the standard
deviation, the narrower the normal curve.
A normal distribution can be defined by its ___ and ______. ✅✅mean and standard deviation
the ___-___-___ rule
con? ✅✅68-95-99.7
However, the rule only works when values are exactly 1, 2, or 3 standard deviations away from the
mean. In order to apply the concept of proportions to other standard deviation values, such as σ = ±
1.4 or σ = ± 2.3, scores or values in the dataset must be standardized.
an exact value that is observed ✅✅raw score
, indicates exactly how many standard deviations a raw score is above or below the mean.
✅✅standard score
describes the exact location of a raw score within the whole distribution when compared to the
mean. It converts each raw score X into a signed, numerical value.
also known as standard scores ✅✅z-score
What does a +z-score mean?
what does a -z-score mean? ✅✅the value from the dataset lies above the mean
the value from the dataset lies below the mean
Coverting raw scores to z-scores ✅✅z= (raw score- mean)/ standard deviation
Converting z-scores to raw scores ✅✅raw score= mean + z * standard deviation
Comparing Values using z-Scores and Raw Scores
When comparing z-scores from the same population or sample, it may be more meaningful to
convert the z-score back to a raw score. For example, compare the performances of the following
students on the physiology exam (μ = 87 , σ = 4 ) given the -scores listed below for Josef, Marco, and
Brooklyn.
Josef: z=-1.75
Marco: z=-2.50
Brooklyn: z=1.25 ✅✅Convert each z-score to a raw score. Then compare the raw scores.
Josef: X=87 - 1.75(4) = 80
Marco: X= 87 - 2.50(4) = 77
Brooklyn: X= 87 + 1.25(4) = 92
z-Scores for Sample Means from a Population ✅✅(sample mean-population mean)/ population
mean/ sqrt(sample size)
