Organizing and Summarizing Data

Chapter 2.1, 2.2

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Frequency Table Frequency Distribution:

• List of each category of data and the number of occurrences for each category

• Frequency – number of occurrences• Usually contains a column with running tally

of occurrences as the are counted• Interval – is used when grouping quantitative

data (also called classes)

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Bar graphs; side by side graphs• Used to compare more than one type of data

at the same time.

3

Histogram• A bar graph of a set of data, constructed from a

frequency table. • The bars are touching (no gap).• If the interval (x-axis) does not start at zero, leave a

break before you make the first bar. • The frequencies (y-axis) are depicted by the height

of a rectangular bars located above the corresponding interval.

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(1) Let’s Make a Freq. Histogram:Using the following list of test scores with 5 classes:

91,87,89,76,84,92,87,88,78,81,89,92,93,86,971) Find the range: 97-76 = 212) Divide the range by 5; 21/5 = 4.2 round up to 5,

thus each interval will go up by 5.3) Create your table with intervals, starting at the

first data value of 76. Add 5 to 76 making your next interval.

4) Tally the occurrences of each interval

Frequency Table from # 1

Interval Tally Frequency

76-80 II 2

81-85 II 2

86-90 IIII I 6

91-95 IIII 4

96-100 I 1

Prb. # 1Example of Histogram

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Frequency

0

1

2

3

4

5

6

7

76-80 81-85 86-90 91-95 96-100

Interval

Fre

qu

ency

WHERE IT'S AT

0

0.5

1

1.5

2

2.5

Turntables Microphones

Items Possessed

Qu

anti

ties

Cumulative Histogram

• Cumulative frequency is the running total of the frequencies. (Add frequencies)

• Rectangular bars getting bigger as you move to the right.

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Pie Chart or Circle Graph

• Circle graph: A graph representing parts of a whole as sectors (pie pieces) of a circle.

• Circle totals 360 degrees of measure.• Proportions can be created to determine

values of the pie pieces or percentages.

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(2) Create a Pie Chart:Using the following amounts spent on books this semester:

Statistics: $138English 101: $94Bowling: $32Psychology: $72Greek Mythology: $481) Find the total amount spent. 2) Determine the percent spent on each (percent must equal 100)3) Find the angle measure associated with each.

Ex. 2 - Table and Circle Graph:Book Percent AngleStats 36 130Eng. 24 86Bowling 8 29Psych 19 68Myth 13 47

Book Expenses

$138

$94

$32

$72

$48

Stats

English

Bowling

Psych.

Myth.

Stem and Leaf Plots

• The leaf is the digit in the place farthest to the right in the number, and the stem is the digit, or digits, in the number that remain when the leaf is dropped.

• To show a one-digit number (such as 9) using a stem-and-leaf plot, use a stem of 0 and a leaf of 9.

• To find the median in a stem-and-leaf plot, count off half the total number of leaves.

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(3) Construct a stem and leaf plot:

- From the following list of data: 10, 18, 12, 22, 43, 23, 11, 51, 16, 27, 11, 44, 32,

29, 30, 26, 14, 46, 11, 19, 24, 36, 40, 31, 25- See board…

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Construct a stem and leaf plot:

• College students spent the following amounts of money on textbooks for one semester.$101, $107, $121, $90, $89, $101, $98, $110, $115, $85, $95, $109, $109, $110, $109, $114

• Find the median from the plot.

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