Advanced Math Topics

2.1-2.2 Frequency Distributions and Histograms

You placed an ad on Craigslist to sell your old car. The following bids were received. Construct a frequency distribution and histogram of the data.$3200 $2375 $3440 $3500 $3230 $3200 $3475 $3200 $3550 $3600

$4000 $3550 $3300 $3600 $3480 $3600 $3525 $3300 $3750 $3800

$3800 $3400 $3950 $3430 $3840 $3950 $3800 $3500 $3600 $3925

$3750 $3625 $3575 $3250 $3980 $3700 $3200 $3950 $3350 $3200

$3900 $3200 $3200 $3700 $3550 $3375 $3900 $3700 $3975 $3200

Frequency distribution-a table that groups data to show meaningful patterns(you can use singletons or intervals)

Histogram(frequency histogram)- a bar graph that has intervals on the horizontal axis and the frequency on the vertical axis

All histograms are bar graphs but not all bar graphs are histograms… http://mathforum.org/library/drmath/view/61175.html

Frequency Table$3200 $2375 $3440 $3500 $3230 $3200 $3475 $3200 $3550 $3600

$4000 $3550 $3300 $3600 $3480 $3600 $3525 $3300 $3750 $3800

$3800 $3400 $3950 $3430 $3840 $3950 $3800 $3500 $3600 $3925

$3750 $3625 $3575 $3250 $3980 $3700 $3200 $3950 $3350 $3200

$3900 $3200 $3200 $3700 $3550 $3375 $3900 $3700 $3975 $3200

1) Find the least and greatest numbers.

2) Between 5 and 15, pick the number of intervals…let’s use 10 intervals.

3) Find the size of the interval by…largest value – smallest value

# intervals= 4000 – 2375

10= 1625

10= 162.5 = 165

Round, make it easier!

Class # Class(Interval)

Car OffersClass Mark Tally Frequency Relative

Frequency

1

2

3

4

5

6

7

8

9

10

$2375-

$2540-$165

$2705-

$2870-

$3035-

$3200-

$3365-

$3530-

$3695-

$3860-

2539

2704

2869

3034

3199

3364

3529

3694

3859

4024

Helps us talk about classes easier!

Lower limit-upper limit

Class Average (midpoint)

2457

2622

2787

2952

3117

3282

3447

3612

3777

3942

I

IIIII IIIII III

IIIII III

IIIII IIIII

IIIII IIII

IIIII IIII

1

0

0

0

0

13

8

10

9

9

Class Frequencytotal frequency

1/50

0

0

0

0

13/50

8/50

10/50

9/50

9/50

average

These are the main columns!!

Rules for Drawing Histograms

1) Intervals are of equal size (except possibly the end intervals)

2) The # of intervals should be 5 through 15

3) Intervals do not overlap. If an interval ends with a counting #, the following interval begins with the next #

4) Any tally falls into 1 and only 1 interval

5) Bars are next to each other. There are no gaps unless an interval has a frequency of 0

Car Offers

FREQUENCY

1

2

3

4

5

6

7

8

9

10

11

$2375- $2540- $2705- $2870- $3035- $3200- $3365- $3530- $3695- $3860-2539 2704 2869 3034 3199 3364 3529 3694 3859 4024

12

13The area under any rectangle compared to the total rectangle areais proportional to the relativefrequency.

9/50

9/50 is the relative frequencyAND 9/50 is the area of this rectanglecompared to the total blue area.

The area of any combination of rectangles is proportional to the sum of their relative frequencies.

13/508/50Add these fractions together to

get 21/50. This is also the sum of theareas of both rectangles divided by thetotal area of all rectangles.

This histogram could help us make decisions about selling our car!!

Here is my tallying suggestion:

$3200 $2375 $3440 $3500 $3230 $3200 $3475

$4000 $3550 $3300 $3600 $3480 $3600 $3525

$3800 $3400 $3950 $3430 $3840 $3950 $3800

$3750 $3625 $3575 $3250 $3980 $3700 $3200

$3900 $3200 $3200 $3700 $3550 $3375 $3900

$2375-

$2540-

$2705-

$2870-

$3035-

$3200-

$3365-

$3530-

$3695-

$3860-

2539

2704

2869

3034

3199

3364

3529

3694

3859

4024

From Assignment 2A Together…

P. 39 #16

57 83 41 55 59 7 77 75 79 84

46 75 68 38 70 82 53 45 60 10

54 23 47 56 79 38 61 23 45 54

21 68 78 74 42 38 97 65 28 67

83 32 54 86 46 45 82 38 42 31

HW P. 35-39 #1, 4, and 16For #4 do the complete table, for #16 do only the

interval and frequency. Create a histogram for both.