Frequency Tables, Line Plots, and Histograms

Nelson/Finizio Algeo I Period 5/6 Quiz Date: 5/11/05 Frequency Tables, Line Plots, and Histograms KEY I. Important Vocabulary 1. Range: the difference between the highest and lowest values 2. Mode: the number or value that occurs the most frequently 3. Median: the number in the middle when data is arranged from least to greatest. 4. Bi-Modal: when you have 2 modes 5. Clusters: data points that are close together 6. Line Plot: a graphic representation in which “x’s” above a number line indicate the frequency of each value 7. Histogram: a graphic representation in which shades boxes above a number line indicate the frequency of each value.

Sample Problem #1 Arrange the following data into a Frequency Table.

Grades students received on their English Exam

73, 53, 78, 93, 100, 72, 79, 84, 97, 92, 56, 93, 72, 93, 93, and 72

Step #1: Set up your Frequency Table. In order to do this you must first list all your number from least to greatest in a frequency table

Grade Tally Frequency 53 1

56 1 Range = 47 72 3

73 1 Mode = 93 78 1

79 1 Median = 79 84 1

Total 16 Sample Problem #2 Using the same data from Sample Problem #1 group the data into intervals.

Grades students received on their English Exam

73, 53, 78, 93, 100, 72, 79, 84, 97, 92, 56, 93, 72, 93, 93, and 72

Grade Tally Frequency 50-59 = F 2

60-69 = D

70-79 = C 6

80-89 = B 1

90-100 = A 7

Total 16

Sample Problem #3 Using the following data create a line plot.

Ages of Mothers of a Class of Students

35, 41, 43, 42, 42, 39, 36, 44, 35, 40, 45, and 42.

Step #1: Figure out what your Range is in this data. In order to do this you must subtract the smallest number from the largest number in you data.

45- 35 10 Range

Step #2: Draw a number line starting with 35 and ending with 59. Place X’s above each number indicating the frequency of each age.

X X X X X X X X X X X X 35 36 37 38 39 40 41 42 43 44 45

Mode = 42 Range = 10 Median = 41.5 Explanation: Since there is an even number of data in this problem (12). You must take the 2 number that are in the middle of the data (41 and 42) and average them. When you do this you get 41.5. Sample Problem #4 Finding Percentage What percentage of the class Mothers is 42 years old? X X X X X X X X X X X X 35 36 37 38 39 40 41 42 43 44 45

Step #1: Look at the line plot and see how many mothers are 42 years old.

In this problem there are 3 mothers that are 42 years old.

Step #2: See how much total data there is.

In this problem there were 12 total data taken.

Step #3: Set up a fraction in which the number of 42 year old Mothers is over the total data taken. In other words how many Mothers out of the total are 42?

3 42 year old Mothers 12 Total number of Mothers

Step #3: Divide 3 by 12.

3 12 .25

Step #4: Change a fraction to a percent. You do this by multiplying by 100 or moving you decimal point 2 spaces to the right. Remember that if you need to round you must round to the nearest percent. Therefore if you were left with 25.6% this would round to 26%

25% of the Mothers of the class are 42 years old.

Sample Problem #5 Create a Histogram using the line plot from Sample Problem #3

Shade in your X’s

X X X X X X X X X X X X 35 36 37 38 39 40 41 42 43 44 45

Sample Problem #6 Find the Range, Mode, and Median

90, 90, 40, 50, 90, 50, 60, 50, and 40

Range: To find the range take the largest number (90) and subtract the smallest number (40) from it.

90- 40 50 Range

Mode: Mode is defined as the number or value that occurs most frequently. In this problem 90 and 50 both occur 3 times. Therefore they will both be the mode (Bi-Modal).

90 & 50 Modes

Median: To find the Median first place the data in order from least to greatest. 40,40,50,50,50,60,90,90,90

Median

Next you must pick out the number that is in the middle of the data. This is your Median.

Practice Problems 1. Arrange the following data into a frequency table.

Judy asked 16 people how many pets they have. She recorded the following data. 2,0,5,1,0,2,6,2,0,3,1,3,4,3,8,3

Pets Tally Frequency 8 7 6 5 4 3 2 1 0

a. How many students have 2 Pets? 3

b. What is the number of pets that most students have? 3

c. How many students have 3 or more pets?

d. What percentage of the students has 3 pets? 25% 2. Arrange the following data into a line plot and histogram The following is a list of NBA franchises and the number of Championships they’ve won Franchise Number of Championships Boston Celtics 16 Minneapolis/ LA Lakers 11 Chicago Bulls 6 Philadelphia/Golden State Warriors 3 Syracuse Nationals/Philadelphia 76ers 3 Detroit Pistons 2 New York Knicks 2 Houston Rockets 2 Milwaukee Bucks 1 Portland Trail Blazers 1

Line Plot

Histogram

Questions

a. What percentage of the franchises won 3 Championships? 20%

b. What is the mode of the data? 2

c. What percentage of the franchises won 2 Championships? 30% d. Do you notice any clusters? If so circle them on your line plot. 3. Arrange the following data in a line plot and histogram. The following is a list of Major League Baseball teams and the number of Championships they’ve won.

Team Championships New York Yankees 26 St. Louis Cardinals 9 Boston Red Sox 6 New York Giants 5 Philadelphia Athletics 5 Pittsburgh Pirates 5 Los Angeles Dodgers 5 Cincinnati Reds 5 Detroit Tigers 4 Oakland Athletics 4

Line Plot

Histogram

Questions a. What percentage of teams won 4 championships? 20%

b. What percentage of teams won 5 championships? 50%

c. What is the mode of the data? 5

d. What is the range of the data? 22

e. Are there any clusters in this data? If so, circle them on your line plot.

f. Do you notice any outliers, if so who is it? New York Yankees 4. Find the Range, Mode, and Median in the following set of data.

25,18,20,25,20,30,35

Range:17

Mode: 20 & 25

Median: 25

5. Find the Range, Mode, and Median in the following set of data.

4.5,4.8,4.2,5.0,4.8,4.1,4.5,4.2,4.8

Range: 0.9

Mode: 4.8

Median: 4.5

6. Find the Range, Mode, and Median in the following set of data.

59,56,61,60,62,63,60,61,63,61,57,60,61,65

Range: 9

Mode: 61

Median: 61