Week 4: The normal distribution curve; Standardised scores

Question 1

How is the standard deviation displayed on a normal distribution (bell curve)? (11 points)

Answer 1

• 68.26% of tested population would fall within ± 1 standard deviation from the mean.
• 95.44% would fall within ± 2 standard deviations from the mean
• 99.72% would fall within ± 3 standard deviations from the mean
• 0.13% of the population would have a standard deviation less than -3
• 2.14% would have a standard deviation that falls between -2 and -3
• 13.59% would have a standard deviation that falls between -1 and -2
• 34.13% would have a standard deviation that falls between 0 and -1
• 34.13% would have a standard deviation that falls between 0 and 1
• 13.59% would have a standard deviation that falls between 1 and 2
• 2.14% would have a standard deviation that falls between 2 and 3
• 0.13% would have a standard deviation greater than 3

Question 2

Describe the various skewed distributions (5 points)

Answer 2

• Skewness = statistical term for the shape of a distribution.
• Leptokurtic = High frequency of scores close to the mean
• Platykurtic= Flat distribution. Not a high frequency of any scores
• Skewed positive = Long tail on positive side. Majority of data sits at a lower rate (to the left) and the tails off to the higher range (right)
• Skewed negative = Long tail on negative side. Majority of data sits at a higher range (to the right) and the tails off to the lower range (left)

Question 3

Where would the mean, median and mode be found on a negatively skewed, positively skewed and normal distribution? (4 points)

Answer 3

• In a normal distribution, the mean median and mode would be very similar to one another and located at the peak of the curve.
• In all three distributions, the mode is located at the peak of the curve.
• In a negatively skewed distribution the median would be slightly less than the mode. The mean would be noticeably less than both the mode and median.
• In a positively skewed distribution the median would be slightly greater than the mode. The mean would be noticeably greater than both the mode and median.

Question 4

Describe Standard Scores (5 points)

Answer 4

• To enable comparison between variables we standardize scores
• When standardizing scores, you calculate:
  
  • Z Scores
  • Percentiles
  • T Scores

Question 5

Describe Z scores (3 points)

Answer 5

• A raw score expressed in standard deviation units
• Equation: Z = (X - mean) / standard deviation
  
  • X = the individual’s score

Question 6

Describe percentiles (4 points)

Answer 6

• What percentage of scores (example Z scores) are below an individual’s score
• Mean (z) = score of 0 which equals percentile of 50
• Positive z score: 50 + corresponding % in table
• Negative z score: 50 - corresponding % in table

Question 7

Describe T-scores (4 points)

Answer 7

• A positive, whole number
• Easy to interpret
• Mean = 50
• T score = 10 x Z + 50