Interval Frequency 30 − 49 3 50 − 69 2 70 − 89 2

90 − 109 1 110 − 129 2

Section 6.1 : Frequency and Histograms

Learning Targets: S.ID.1, N.Q.1, S.ID.3

Important Terms and Definitions

Frequency of an Interval: the number of data values in that interval

• Intervals should not overlap or have any gaps

Frequency Table: groups a set of data values into intervals and shows the frequency for each of the intervals

Cumulative Frequency Table: shows the number of data values that lie in or below a given interval

Histogram: A graph that gives a visual representation of the data in a frequency table. It has one bar for each interval, and the height of the bar shows the frequency of data in that interval

• There are no gaps between bars, and the bars are of equal width • There are three different ways to classify histograms by their shape

o Uniform : All of the bars are roughly the same height o Symmetric: A vertical line can divide the histogram into two parts that are close to

mirror images o Skewed: It has one peak that is not in the center

Example: The following data gives the amount of time certain teenagers spent on the internet in minutes/day. Make a frequency table, histogram, and cumulative frequency table of the data.

75, 38, 43, 120, 65, 48, 52, 115, 96, 87

Frequency Table Histogram

0

1

2

3

4

30-49 50-69 70-89 90-109 110-129

Note: This histogram would be classified as skew

Interval Frequency Cumulative Frequency

30 − 49 3 3 50 − 69 2 5 70 − 89 2 7

90 − 109 1 8 110 − 129 2 10

Cumulative Frequency Table

(ex 1) Make a frequency table, histogram, and cumulative frequency table of the following half marathon times (given in minutes). Also, classify the histogram as uniform, symmetric, or skew.

135, 211, 220, 180, 175, 161, 246, 201, 192, 167, 235, 208

(ex 2) The Bugle did a survey to determine how many clubs/teams to which students belong. The results of the survey are shown in the histogram. What does the height of each bar represent? Approximately how many total students were surveyed?

01020304050

0-4 5-9 10-14 15-19

(ex 3) The following set of data shows the number of dollars Zach spent on lunch each day for the past two weeks. Make a frequency table, histogram, and cumulative frequency table to represent the data. Also, classify the histogram as uniform, symmetric, or skew. How much money should Zach bring for lunch next week? Why?

17, 1, 4, 11, 14, 14, 5, 16, 6, 5, 9, 10, 13, 9

(ex 4) Make a frequency table, histogram, and cumulative frequency table of the following earthquake magnitudes. Also, classify the histogram as uniform, symmetric, or skew.

2.1, 5.4, 6.7, 3.2, 4.5, 2.7, 2.6, 3.1, 4.4, 8.1, 4.1, 2.9, 2.1

Homework – Section 6.1 : Frequency and Histograms

Make a frequency table, histogram, and cumulative frequency table of each of the data sets. Also, classify each histogram as uniform, symmetric, or skew.

1. Average souvenir t-shirt prices at beach shops in Myrtle Beach 9, 10, 12, 9, 18, 12, 13, 10, 5, 8, 16, 11

2. Average number of students per class for different teachers 24, 19, 14, 25, 26, 26, 16, 19, 22, 21, 27, 29, 15, 24

3. Battery life, in hours, for different brands of batteries 12, 9, 10, 14, 10, 11, 10 18, 21, 10, 14, 22

4. Number of television shows watched on a weekly basis by surveyed students 3, 7, 9, 4, 1, 0, 2, 5, 4, 2, 3, 1, 0, 8, 14, 5, 6

5. The following data set represents test scores in your class from the Chapter 5 Test. Create three different histograms to represent the data: one with intervals of 5, another with intervals of 10, and the last one with intervals of 20. If you wanted to present the data and make it seem as though there were little variation in the test scores, which histogram would you use?

81, 70, 73, 89, 68, 79, 91, 59, 77, 73, 80, 75, 88, 65, 82, 94, 77, 67, 82

6. The track list for One Direction’s Take Me Home album is shown below. Make a cumulative frequency table that represents the lengths of the songs in seconds. About what percentage of the songs are under 3 minutes? How do you know?

Track/Length info from Wikipedia

Interval Frequency Cumulative Frequency

0 − 9 6 10 − 19 18

20 − 29 26

30 − 39 34

7. Complete the cumulative frequency table shown below.

8. This histogram below shows the amounts of money that 50 customers spent at Sam’s Club this weekend. What is the upper limit on the amount of money that any customer spent? Which interval represents the greatest number of customers? How many customers spent less than $60?

0

4

8

12

16

0-19 20-39 40-59 60-79 80-99

Sam's Club Spending