Averages And Spread

Question 1

What is an average also called?

Answer 1

Measure of central tendency

Question 2

What is x̄?

Answer 2

The mean (x bar)

Question 3

What is it called when you have two modes?

Answer 3

Bimodal

Question 4

What is Q1?

Answer 4

The lower quartile

Question 5

What is Q2?

Answer 5

The median

Question 6

What is Q3?

Answer 6

Upper quartile

Question 7

What is the median?

Answer 7

The middle value when the data is in order.

Question 8

What is the lower quartile?

Answer 8

One quarter of the way through a data set.

Question 9

What is the upper quartile?

Answer 9

Three quarters of the way through the data set.

Question 10

What is a measure of spread?

Answer 10

A measure of how spread out the data is.
eg range, IQRange

Question 11

What is the advantage and disadvantage of using the range as a measure of spread?

Answer 11

Takes all the data into account but can be affected by extreme values.

Question 12

What is the advantage of using the interquartile range as a measure of spread?

Answer 12

It’s not affected by extreme values but only considers the spread of the middle 50% of the data.

Question 13

What is standard deviation (σ) equal to?

Answer 13

The square root of variance

Question 14

What do standard deviation and variance show?

Answer 14

The dispersion of values around the mean. Standard deviation gives a kind of ‘average’ amount by which all the values deviate from the mean.

Question 15

What is the best measure of spread?

Answer 15

Standard deviation / variance.

Question 16

What does Σx mean?

Answer 16

Sum of the x values.

Question 17

What does Σx^2 mean?

Answer 17

Sum of the x^2 values.

Question 18

What does σ^2 x mean?

Answer 18

Variance

Question 19

What does σx mean?

Answer 19

Standard deviation

Question 20

What does n mean?

Answer 20

Number in data set.

Question 21

What does min(x) mean?

Answer 21

Smallest data value

Question 22

What does max(x) mean?

Answer 22

Largest data value

Question 23

What is an outlier?

Answer 23

An extreme value that lies outside the overall pattern of data.

Question 24

What is a common definition of an outlier?

Answer 24

• Greater than Q3 + k(Q3 -Q1)
Or
• Less than Q1 - k(Q3 - Q1)

Question 25

What is (Q3 - Q1)?

Answer 25

The interquartile range.

Question 26

Are there sometimes outliers that are legitimate values?

Answer 26

Yes

Question 27

When outliers are a mistake, what are they called?

Answer 27

Anomalies

Question 28

What is the process of removing anomalies from a data set known as?

Answer 28

Cleaning the data.

Question 29

What must you do when removing anomalies?

Answer 29

Justify why it is an anomalie and not just an outlier.

Question 30

What does a box plot show?

Answer 30

•median
•quartile
• max and min values
•outliers

Question 31

When comparing 2 box plots what should you consider?

Answer 31

• median as a measure of average
• IQR as a measure of spread
• outliers
• symmetry

Question 32

What is a symmetrical box plot?

Answer 32

When the median is in the middle of the box, there is no skew.
Q3 - Q2 = Q2 - Q1

Question 33

What is a positive skew box plot?

Answer 33

When the median is to the left of the box.
Q3 - Q2 > Q2 - Q1

Question 34

What is a negative skew box blot?

Answer 34

When the median is to the right of the box.
O3 - Q2 < Q2 - Q1

Question 35

In a histogram, what is the area of the bar proportional to?

Answer 35

The frequency in each class.