Topic 4: intro to measurement of frequency distributions

Question 1

Describe the frequency distribution for a histogram

Answer 1

• To describe the distribution = look at over all pattern
• Over all pattern = shape + spread + center
• Line connected = too detailed
• Smoothed curve = highlights distribution

Question 2

Types of distribution for numeric variables

Answer 2

• Unimodal = 1 peak
• Bimodal = 2 peaks
• Multimodal = many peaks
• Normal = symmetrical = bell-shaped where both sides are mirror images
• Positively skewed = right side extends like tail
• Negatively skewed = left side extends like tail

Question 3

Describe the central tendency measure in negative skew

Answer 3

• Mode = peak
• Median = shifts to left of mode
• Mean = middle of dip to the left

Question 4

Describe the central tendency measure in positive skew

Answer 4

• Mode = peak
• Median = shift to right of mode
• Mean = middle of dip to the right

Question 5

Describe the central tendency measure in normal distribution

Answer 5

• Mean=mode=median
• Data is distributed around mean = most common distribution value also there + it is the middle point of curve

Question 6

Define outliers

Answer 6

• Observations that lie outside overall pattern of distribution

Question 7

What is the effect of outliner on the mean/median?

Answer 7

• The mean is either pulled to the right or left depending on where the outlier is
• Median is largely unaffected

Question 8

How do you know when boxplot is skewed?

Answer 8

• The box will not align in the middle of the lines
• If it is extended more to the right/above = positive skew
• If it is extended more to left/below = negative skew

Question 9

How does distribution affect choice of summary statistics?

Answer 9

• Mean = should only be used in normal distribution = affected by skew/outlier
• In large sample = outlier won’t affect mean = can be used BUT skewness always affects mean even in large
• SD = only use in normal distribution = affected same as mean
• Median/IQR = used when skew/outliers
• Mode = infrequently used in scientific research

Question 10

How to use SD to estimate range of a distribution

Answer 10

• Mean + (1 x SD)
• Mean - (1 x SD)
• Gives you range

Question 11

How to calculate range that covers 95% of values in sample

Answer 11

• Mean + (1.96 x SD)
• Mean - (1.96 x SD)
• Gives you range