Data and Distribution

You will review/learn:

• ways of organizing discrete data

• recognize outlier

• describe distribution of data set

Length of Calls in Minutes

Number of Calls

Tally Frequency

3 / 1

4 /// 3

5 0

6 // 2

7 //// 5

8 //// // 7

9 //// 4

10 / 1

Tally Chart

Look at this tally chart.

How many 7 minute phone calls were made?

5 phone calls

How do you know?

There were 5 tally marks in the 7 minute row so the frequency was 5.

X

X

X X

X X X

X X X X

X X X X X

X X X X X X X

3 4 5 6 7 8 9 10

Number of Phone Calls

Length of Calls in Minutes

Look at this line plot. How many 10 minute phone calls took place?

1 phone call

Where does most of the data cluster? What does this tell you?

Most of the date clusters from 7 – 9 minutes. Most of the phone calls were 7 to 9 minutes long.

Where is the gap in the line plot? What does this tell you?

There is a gap at 5. No one made a phone call lasting 5 minutes.

X

X

X X

X X X

X X X X

X X X X X

X X X X X X X

3 4 5 6 7 8 9 10Length of Calls in Minutes

Number of Phone Calls

Stem and Leaf Plot

A Stem and Leaf Plot is a method of organizing intervals or groups of data.

Here is an example:

Key: 3 | 6 = 36

A stem and leaf plot allows you to see easily the greatest, least, and median values in a set of data. It gives you a quick way of checking how many pieces of data fall in various ranges. It also lets you see the value of every piece of data.

 

How many students’ heights were measured?

19 students

How many students are taller than 56 inches?

10 students

What is the height of the tallest student?

63 inches

What is the mode of the students’ heights?

57 inches

What is the range of the students’ heights?

16 inches

What is the median student height?

57 inches

4 7 8 8 9 9

5 2 4 4 5 7 7 7 8 9 9

6 0 0 1 3

Key: 4 l 7 means 47 inches

Look at this Stem and Leaf Plot and answer

the questions.

Draw your own Stem and Leaf Plot

Here is the information for your Stem and Leaf Plot.

Yesterday, Tina’s teacher kept track of how many ounces of milk each student drank in one day. Here is the data she collected: 12, 20, 8, 32, 24, 32, 36, 21, 28, 32.

Don’t forget a title for your graph. Remember to label!

Milk Drunk in One Day

0 8

1 2

2 0 1 4 8

3 2 2 2 6

Key: 1 l 2 means 12 ounces

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Outliers

• data values that are either much larger or much smaller than the general body of data

• appears separated from the body of data on a frequency graph

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2 3 4 5 6 7

1520

2530

35

x

y

2 3 4 5 6 7

1520

2530

35

x

y

0 1 2 3 4 5 6

05

1015

2025

30

x

y

0 1 2 3 4 5 6

05

1015

2025

30

x

y

No outliers

No high-leverage

points

Low leverage

Outlier: big residual

High leverag

eoutlier High-

leverage outlier

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Example: outlier (3D)

3000 3500 4000 4500 5000 5500 6000

200

250

300

350

400

450

500

550

280

300

320

340

360

380

400

percap

un

de

r18ed

uc

High leverage

point

The Normal Distribution

CA

If the three histograms shown below represent the marks scored by students sitting 3 different tests, comment briefly on the difficulty level of each test.

Left-Skewed

Right-Skewed

Symmetrical

Easy

Difficult

In test A most students scored high marks.

In test B the marks are evenly distributed.

B Normal

In histogram B, most students found the

test neither easy nor

difficult.

This type of distribution occurs often and is known as the NORMAL distribution. It is characterized by the bell-shaped curve that can be drawn through the top of each bar.

In test C most students scored Low marks.

The Normal Distribution

Which of the distribution below are approximately, normal, right or left skewed.A B C

D E F

G H I

Right Skewed

Right Skewed

Left SkewedNormal

Normal

Normal

Neither

Neither

Neither