Basic Statistics Review

A statistical question....

• Requires you to gather data

• Is not a yes or no question

• One that can be answered by collecting multiple data and where there will be opportunity for variability in that data.

• Statistics is the process of collecting, organizing, and interpreting pieces of information, or data.

• Statistical Questions: are questions that anticipate and accounts for a VARIETY of answers.

Multiple Choice

How long did it take for each person to get to to school?

• Statistical

• Non-statistical

Multiple Choice

How many siblings do you have?

• Statistical

• Non-statistical

Multiple Choice

What is your favorite color?

• Statistical

• Non-statistical

Multiple Choice

How many books do each student in your class have?

• Statistical

• Non-statistical

Multiple Choice

What is the average or typical number of Chromebooks each student was given by the school?

• Statistical

• Non-statistical

Multiple Choice

What is the average or typical number dogs in each Kennedy family?

• Statistical

• Non-statistical

Dot Plots

Each dot represents one answer. In the sheet to the right, 3 students answered that they had 0 cookies at lunch. 5 said they had 2 cookies.

Multiple Choice

This is a

• dot plot

• frequency table

• relative frequency table

• histogram

Outlier

If there is a number far from the normal set, we call that the outlier.

1,10,12,15,16

The outlier is 1.

Multiple Choice

What is the outlier for this data?

• 90

• 96

• 102

• 108

Multiple Choice

How many students took the quiz? (count the dots)

• 15

• 20

• 12

• 17

Shape of a dot plot graph

Normal is like a symmetrical hill or an upside-down U.

Skewed Right

Think of it like a tail. If the numbers decrease on the right side of a graph, the tail goes to the right, and the graph is skewed right.

Skewed Left

Our tail is on the left side. We say that these graphs are skewed left.

Multiple Choice

Are these dot plots symmetric?

• Yes
• No

Multiple Choice

Which statement correctly describes the shapes of the dot plots for cars and SUVs?

• SUVs: Symmetrical
  Cars: Skewed left

• Both are skewed left.

• Both are symmetrical.

• SUVs: Skewed right
  Cars: Skewed left

Multiple Choice

Is the Cars dot plot skewed left or right?

• left
• right

Multiple Choice

How many students received a score of 94%? 

• 94
• 4
• 1
• 2

Multiple Choice

What is the outlier for this data?

• 90

• 96

• 102

• 108

We can use the dot plot to find Mean, Median, and Mode

Remember, write out all your numbers in numerical order then solve the problem.

Multiple Choice

What is the median of the data?

• 2

• 1

• 3

• 12

Multiple Choice

What is the MEDIAN of this data?

• 65
• 40
• 915
• 13

Multiple Choice

What is the range of the test scores?

• 15
• 100
• 6
• 10

Multiple Choice

What is the MODE of this data?

• 90
• 85, 90, and 95
• 85 and 95
• None

Multiple Choice

What is the highest score anyone in the class received on the test?

• 89%

• 100%

• 95%

• 98%

Multiple Choice

What was the most common score the students got on the test (the mode)?

• 88%

• 100%

• 89%

• 98%

Skewed Left or Right

• When a distribution is skewed left, the mean is less than the median.

• When a distribution is skewed right, the mean will be more than the median.

Bell or Symmetrical Distributions

• Symmetrical distributions of data can also be called normal or bell-shaped.

• Since their distribution is fairly normal, the mean and the median will be close to the same.

Multiple Choice

Describe the shape of the distribution.

• symmetric

• skewed left

• skewed right

Multiple Choice

How many students had more than 6 candy bars?

• 5

• 2

• 3

• 1

Multiple Choice

How many cars were sold on Saturday and Sunday?

• 5

• 3

• 8

• 10

Multiple Choice

How many of the rings are ¼ carat or less?

• 2
• 4
• 6
• 8

Multiple Choice

How many students have 0 Brothers and Sisters?

• 6 students

• 0 students

• 12 students

• 10 students

​Box Plot Diagram

Multiple Choice

What amount of cupcakes makes up the middle 50% of the data?

• 16-22 cupcakes

• 12-32 cupcakes

• 22-28 cupcakes

• 16-28 cupcakes

Multiple Choice

What amount of cupcakes makes up the lower 25% of the data?

• 16-22 cupcakes

• 12-16 cupcakes

• 22-28 cupcakes

• 28-32 cupcakes

5 Number Summary

We use the five number summary to create and help interpret data from a box plot.  The 5 number summary includes:  Minimum, Maximum, (Q1) Quartile 1 or Lower Quartile, (Q2) Median, and (Q3) Quartile or Upper Quartile.

Parts of a Box Plot

• Min – Minimum: Smallest number of the Data Set

• Q1 – Lower Quartile:  The median of the lower half of the data

• Q2 – Median:   Middle number of the set of data

• Q3 – Upper Quartile:  The median of the upper half of the data

• Max – Maximum:  Largest number in the data set

• Interquartile Range (IQR): Q3 – Q1

Multiple Choice

What does a box plot NOT allow you to find?

• Median

• Mean

• Range

• Interquartile Range (IQR)

• Q1 and Q2

Quartiles

• Quartiles divide the data set into four equal parts.

• 25% each

Median

• Divides the data set into two halves

• 50% of the data numbers are below this number

• 50% of the data numbers are above this number

Multiple Choice

Which teaching method had the most variability of scores (most stretched out)?

• Method 1

• Method 2

• Method 3

• Method 4

Multiple Choice

Which 5 number summary matches the box plot?

Multiple Choice

The box plot shows the distribution of scores on a math test. Which score was greater than or equal to 75% of all scores?

• 100

• 90

• 65

• 70

Multiple Choice

The box plot shows finishing times for a local 5K race. Between what times did 50% of the runners finish?

• 14 to 26 minutes

• 14 to 21 minutes

• 12 to 26 minutes

• 21 to 26 minutes

• Not enough information

Multiple Choice

The box plot shows finishing times for a local 5K race. Between what times do 75% of the runners finish?

• 14 to 26 minutes

• 14 to 21 minutes

• 12 to 26 minutes

• 21 to 26 minutes

Multiple Choice

What number represents the lower extreme or minimum? / ¿Qué número representa el extremo inferior o el mínimo?

• 13

• 16

• 23

• 25

Multiple Choice

What is the median shown on this graph? / ¿Cuál es la mediana que se muestra en este gráfico?

• 200

• 250

• 500

• 720

Multiple Choice

What is the upper quartile? / ¿Qué es el cuartil superior?

• 20

• 30

• 70

• 95

Multiple Choice

What is the upper quartile shown in this graph? / ¿Cuál es el cuartil superior que se muestra en este gráfico?

• 18

• 21

• 21.5

• 23

Multiple Choice

What percentage of the data is between 30 and 70?

• 25%

• 50%

• 75%

• 100%

Multiple Choice

What percentage of the data is between 20 and 80?

• 25%

• 50%

• 75%

• 100%

• The Box and Whisker plot is divided in to 4 parts.

• Each Part is 25% of the data set or ¼.

Analyzing the Data Set

Multiple Choice

What percentage of the data is Below 30?

• 25%

• 50%

• 75%

• 100%

Multiple Choice

What percentage of the data is greater than 30?

• 25%

• 50%

• 75%

• 100%

Multiple Choice

What is the maximum value?

• 58
• 66
• 64
• 60

Box Plot

​​The five-number summary:

Min: Minimum or lowest number in the data set
Max: Maximum or highest number in the data set
Median: The value in the middle of the data set when the numbers are in order from least to greatest
Lower Quartile: The median of the lower half of the data when the numbers are in order
Upper Quartile: The median of the upper half of the data when the numbers are in order

Multiple Choice

​I can use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

What is the most common amount of siblings to have shown in the histogram?

• 0

• 1

• 4

• 5

Multiple Choice

What is the interquartile range (IQR)?

• 4
• 64
• 60
• 8

Multiple Choice

between what ages were the least amount of people at the bowling alley?

• 6-15

• 16-25

• 26-35

• 36-45

Multiple Choice

How many times did she practice for less than 30 minutes?

• 13

• 9

• 12

• 17

Multiple Choice

How many students have more than 1,000 songs on their MP3 player?

• 5
• 16
• 10
• 4

Multiple Choice

In which interval is the peak of the data?

• 0 to 4

• 5 to 9

• 10 to 14

• 15 to 19

• 20 to 24

Multiple Choice

Which interval has exactly 400 employees?

• 33-43

• 0-10

• 77-87

• 66-76

You can use histograms to determine how your data is distributed and/or skewed. You consider the MEAN and the MODE of the data set.

​

Definition

​Left-Tailed Skewed

The bulk of the observations are at or above the median but there are a few observations that are much smaller than the rest.

Right-Tailed Skewed

The bulk of the observations are at or below the median but there are a few observations that are much larger than the rest.

Multiple Choice

Find the mean of these numbers:
2, 57, 38, 42, 6

• 29
• 38
• 50
• 145

Multiple Choice

The height of three basketball players is 210 cm, 220 cm and 191 cm.
What is their average height?

• 210
• 207
• 220
• 200

Multiple Choice

Find the mean giraffe heights.

• 15

• 15.5

• 15.7

• 28.2

Multiple Choice

What is the MEAN for this data?

• 80
• 1040
• 13
• 81

Multiple Choice

The temperature in Michigan City on this date in the last ten years were: 68, 68, 69, 70, 72, 70, 68, 75, 55, 67. What is the mean temperature on this date over the last ten years? (Round to nearest whole number.)

• 60

• 61

• 68

• 69

Multiple Choice

Find the mean of these numbers:
5,11,2,12,4,2

• 4.1
• 6
• 4.5
• 4

Multiple Choice

Find the mean:
28, 18, 19, 18, 17

• 20
• 18
• 11
• 19

Multiple Choice

Calculate the mean.

10, 4, 5, 9

• 7

• 5

• 8

• 4

Multiple Choice

What is the MEAN for this data?

• 80
• 1040
• 13
• 81

Multiple Choice

What is the MODE for this data?

• 80
• 85

• 13
• 81

Multiple Choice

What is the MEDIAN of this data?

• 65
• 40
• 915
• 13

Multiple Choice

What is the MODE of this data?

• 65
• 40
• 60

• 13

Multiple Choice

To get the ______, add up all the numbers in a data set and divide by the amount of numbers in the data set.

• Median

• Mean

• Mode

• Range

Multiple Choice

To get the ________, subtract the smallest number in the data set from the biggest number in the data set.

• Mean

• Median

• Mode

• Range

Multiple Choice

To get the _______, order the numbers in the data set from smallest to biggest and find the middle number in the data set.

• Mean

• Median

• Mode

• Range

Multiple Choice

To get the ________, select the number that occurs the most in a data set aka the most popular number.

• Mean

• Median

• Mode

• Range

Multiple Choice

Find the Mean of the Data Set:

7, 8, 3, 4, 8

• 7

• 6

• 5

• 4

MEDIAN

Order the numbers from least to greatest, then select the number in the middle.

Multiple Choice

Find the Median in the Data Set:

7, 8, 3, 4, 8

• 7

• 8

• 4

• 3

MODE

a.k.a. The Most Popular Number

RANGE

Subtract the lowest number from the highest number.