Quantitative Data part 1

Distribution

• What value a variable takes and how often it takes that value

Dot Plots

• Show count associated with a value
• Stacks of dots over a numerical value
• Good for small data sets

Description for FRQ:

Largest category, symmetry, skewness, clusters, gaps, outliers

Stem and Leaf plot

• Stems are larger digit places, leaves are smaller digit places
• Good for small amounts of data

Description for FRQ:

Center, spread, shape, unusual features

Histograms

• Summarize large sets of data and grouped into intervals
• Vertical axis indicates frequencies or relative frequencies
• Horizontal axis indicates data values or ranges of data values
• Number of data variables in any interval is the frequency of the interval
• Unless there are no observations, there’s no gap between bars

Description for FRQ:

Skewed left/right, bell/mound shape, rectangular, uni/bi modal

Mode

• “most”
• A value or set of values that occurs most frequently
• The mode is where a frequency distribution reaches a maximum
• Bimodal- 2 modes
• Multimodal- multiple modes
• Not always near center of distribution

Median

• (Q2) middle value when observations are in numerical order
• If there are 2 middle numbers, then add the two numbers and average them
• If the distribution if symmetrical, then mean and median are equal
• The median is resistant because outliers don’t or barely affect value
• This means that when there are outliers, the median is a better measure of the center

Mean

Population parameter: μ (mew)

Sample statistic: x̄ (x_bar)

• Add all the data points and divide by number of data points

  x̄ = (∑xi)/n = (x1+x2+x3+ ……..+xn)/n

  n= number of data items

  ∑= sum of whatever follows

• Balance point of distribution

• The mean is non resistant because outliers affect it

Symmetry

• The right and left halves mirror each other
• The mean and median are equal

Skewness

• If the right tail is longer than the left, then it is a right/positive skew and mean > median
• If the left tail is longer than the right, then it is a left/negative skew and mean < median

Measures of Dispersion

Used to describe spread of data/variation around a central value

Range

• The difference between the biggest and smallest number
• It is not resistant to the influence of outliers

\