Chapter 2

• Section 2.1: Organizing qualitative data• Section 2.2: Organizing quantitative data• Section 2.3: skip• Section 2.4: Misrepresentations of data

Qualitative vs. Quantitative (Different tools for different data)

• Question 1: Type of skin cancer– A: Qualitative– B: Quantitative

Qualitative vs. Quantitative (Different tools for different data)

• Question 1: Type of skin cancer– A: Qualitative– B: Quantitative

• Question 2: Quarterly profit – A: Qualitative– B: Quantitative

Qualitative vs. Quantitative (Different tools for different data)

• Question 1: Type of skin cancer– A: Qualitative– B: Quantitative

• Question 2: Quarterly profit – A: Qualitative– B: Quantitative

• Question 3: Customer satisfaction– A: Qualitative– B: Quantitative

Qualitative vs. Quantitative (Different tools for different data)

• Question 1: Type of skin cancer– A: Qualitative– B: Quantitative

• Question 2: Quarterly profit – A: Qualitative– B: Quantitative

• Question 3: Customer satisfaction– A: Qualitative (poor, moderate, high)– B: Quantitative (1,2,3,4,5,6,7,8,9,10)

It isn’t always totally clear!

• Frequency: A fancy word for “count”

• Frequency: A fancy word for “count”• Distribution: A way to describe how likely

certain values are to be observed.

• Frequency: A fancy word for “count”• Distribution: A way to describe how likely

certain values are to be observed.• Frequency distribution: A list tabulating the

number of occurrences for each category

• Frequency: A fancy word for “count”• Distribution: A way to describe how likely

certain values are to be observed.• Frequency distribution: A list tabulating the

number of occurrences for each category• Relative frequency distribution: A frequency

distribution that uses proportions instead of counts.

Which is a relative frequency table?Statistics 108 students’ class standings (n=79)

Class standingFreshmen 0.5000

Sophomore 0.1500

Junior 0.1750

Senior 0.1625

A

B

SophomoreSeniorJuniorFreshman

50

40

30

20

10

0

Class

Perc

ent

Stat 108 students

Percent within all data.

These graphs are:(A)bar graphs (B)histograms

Which graph is the relative frequency graph? (A) top graph(B) bottom graph

• The only difference between a frequency bar graph and a relative frequency bar graph is the labeling of the y-axis. (Likewise for histograms.)

• Relative frequency saves the reader calculations

• Frequency graphs tell the reader the actual counts.

A pie chart of the data

Fr

So

Jr

Sr

Use the below data to calculate degrees of the sophomore slice.

(A)12 degrees(B)0.15 degrees(C)15 degrees(D)55 degrees

Histograms

• Histograms are for quantitative data• “Classes” or “bins” are which data are

grouped into.• Upper and lower limit for each class/bin is

subjective.• Goal: Summarize data, but leave some detail.

Histograms of sparrow weights

Moderate number of bins

Freq

uenc

y

22 24 26 28 30 32

010

20

lots of bins

Freq

uenc

y

22 24 26 28 30 32

05

1015

Weights of 87 sparrows (grams)23.2 23.3 23.3 23.5 23.6 23.7 23.8 23.9 24 24.1 24.2 24.3 24.3 24.3 24.4 24.5 24.6 24.6 24.6 24.6 24.7 24.7 24.7 24.8 24.8 24.9 24.9 24.9 25 25 25 25.1 25.4 25.5 25.5 25.6 25.6 25.6 25.7 25.7 25.7 25.7 25.7 25.8 25.9 25.9 26 26 26 26 26 26.1 26.1 26.2 26.2 26.3 26.3 26.4 26.5 26.5 26.5 26.5 26.6 26.6 26.7 26.7 26.7 26.8 26.8 26.9 26.9 26.9 26.9 27 27 27.1 27.3 27.5 27.5 27.6 27.9 28 28.3 28.3 28.6 29 31

Stem-and-leaf plot

In the below software’s stem-and-leaf plot, the decimal point is at the | Displays vary slightly across statistical software

23 | 23356789 24 | 01233345666677788999 25 | 000145566677777899 26 | 000001122334555566777889999 27 | 00135569 28 | 0336 29 | 0 30 | 31 | 0

Determine the original data set:(The decimal point is 1 digit(s) to the right of the |)

0| 234 0 | 5889 1 | 000134444 1 | 578 2 | 00(A) 0.2, 0.3, 0.4, 0.5, 0.8, 0.8, 0.9, 1, 1, 1, 1.1, 1.3, 1.4, 1.4, 1.4, 1.4, 1.5, 1.7,

1.8, 2, 2 (B) 2, 3, 4, 5, 8, 8, 9, 10, 10, 10, 11, 13, 14, 14, 14, 14, 15, 17, 18, 20, 20(C) 234, 5889, 1000, 1001, 1003, 1004, 1004, 1004, 1004, 1004, 1587, 200(D) 0.234, 0.5889, 1.000134444, 1.578, 2.00

Create a stem-and-leaf plot for values:24,25,26,29,29,30,31,31,35,36,36

2 | 4 2 | 5699 3 | 011 3 | 566

2 | 45699 3 | 011566

Dot Plot

Sparrow weights (grams)

Cou

nt

0

5

10

15

20

25

24 26 28 30

Bad graphs…