MA

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