Displaying Distributions – Quantitative Variables Lecture 13 Secs. 4.4.1 – 4.4.3 Mon, Sep 25, 2006

Frequency Plots Frequency Plot – A display of quantitative data in which X’s are drawn over the scale to represent the values. Draw the real line. Mark the minimum and maximum values. Label the values on the scale, as on a ruler. Mark at regular intervals. For each data value, draw an X over that value on the scale.

Uniform Random Numbers Use randInt(1,10,50) to get 50 random integers from 1 to 10. Store the list in L1. Sort them into ascending order. Draw a frequency plot of the data.

TI-83 Press 2nd STAT PLOT. Press ENTER to select Plot1. Turn Plot1 On. Select the histogram icon. Enter L1 as the list (Xlist). Freq should be 1. continued…

TI-83 Press WINDOW. Set Press GRAPH. A graph should appear. Xmin = 0. Xmax = 11. Ymin = -1. Ymax = 15. Press GRAPH. A graph should appear. Use TRACE to get the frequencies.

Frequency Plots What information is conveyed by a frequency plot?

Shapes of Distributions Symmetric – The left side is a mirror image of the right side. Unimodal – A single peak, showing the most common values. Bimodal – Two peaks. Uniform – All values have equal frequency. Skewed – Stretched out more on one side than the other.

Stem-and-Leaf Displays Each value is split into two parts: a stem and a leaf. For example, the value 1.23 could be split as stem = 12, leaf = 3, or stem = 1, leaf = 2, or stem = 0, leaf = 1. The stem consists of the leftmost digits of the value, as many as deemed appropriate. The leaf consists of the next digit (one digit).

Stem-and-Leaf Displays A note should be added indicating how to interpret the numbers. Note: 12|3 means 1.23.

Stem-and-Leaf Displays A note should be added indicating how to interpret the numbers. Note: 12|3 means 1.23. stem leaf actual value

Splitting the Numbers We choose where to split the numbers in order to avoid Too many stems, each with too few leaves. Too few stems, each with too many leaves.

Example Draw a stem and leaf display of the following GPAs. 2.946 2.335 3.418 1.890 2.731 3.855 1.344 2.126 2.881 2.542 2.504 3.367 1.950 2.392 2.443 3.053

Example We may split the values at the decimal point: Note: 1|2 means 1.2. 1 2 3 3 8 9 1 3 3 4 5 5 7 8 9 0 3 4 8

Example We may split the values at the decimal point: Note: 1|2 means 1.2. 1 2 3 3 8 9 1 3 3 4 5 5 7 8 9 0 3 4 8

Example Or we may split the values after the first decimal place: 13 14 15 4 16 17 18 19 20 : 9 5 Note: 12|3 means 1.23.

Example Or we may split the values after the first decimal place: 13 14 15 4 16 17 18 19 20 : 9 5 Note: 12|3 means 1.23.

Example Which is better? Is either one particularly good?

Stem Splitting We can obtain a good compromise (in this examle) by splitting the stems. Each stems appears twice. The first time for leaves 0 – 4. The second time for leaves 5 – 9.

Stem Splitting Note: 1|2 means 1.2. 1 2 3 8 9 1 3 3 4 5 5 7 8 9 0 3 4

Stem Splitting Note: 1|2 means 1.2. 1 2 3 8 9 1 3 3 4 5 5 7 8 9 0 3 4

Shapes of Distributions What shape would you expect a distribution of random numbers to have? Why? What shape would you expect a distribution of household incomes to have? Why? What shape would you expect a grade distribution to have? What shape would you expect a distribution of heights of adults to have?