Statistics - Location and spread

Question 1

What is a measure of location?

Answer 1

Single value which describes a position in a data set

Question 2

What is a measure of central tendency?

Answer 2

Single value that describes the centre of the data

Question 3

What is the mean?

Answer 3

Sum of data values / number of data values

Question 4

What is the median?

Answer 4

The middle value when the data values are put in order

Question 5

What is mode?

Answer 5

The value or class that occurs most often

Question 6

When should median be used?

Answer 6

Used when there are extreme values

Quantitative data

Question 7

When should mean be used?

Answer 7

Quantitative to represent all data

But affected by extremes

Question 8

When should mode be used?

Answer 8

Qualitative or quantitative
Either one or two modes
Not very informative if each value occurs once

Question 9

How can the mean of data in a frequency table be calculated?

Answer 9

Mean = Sum of products of data and their frequencies / sum of the frequencies

Question 10

What is the lower quartile?

Answer 10

Q1

One-quarter of the way through the data set

Question 11

What is the upper quartile?

Answer 11

Q3

Three-quarters of the way through the data set

Question 12

How is data split if there is a 85th percentile?

Answer 12

85% of data is less than 85th

15% of data is more than 85th

Question 13

How can you calculate the lower quartile for discrete data?

Answer 13

n/4
If whole number, Q1 is halfway between this point and the one above
If not whole number, round UP and pick this data point

Question 14

How can you calculate the upper quartile for discrete data?

Answer 14

3n/4
If whole number, Q3 is halfway between this point and the one above
If not whole number, round UP and pick this data point

Question 15

How can you calculate Q1-3 for cumulative frequency table?

Answer 15

Q1 = n/4 th data set
Q2 = n/2 th data set
Q3 = 3n/4 th data set
NO ROUNDING

Question 16

Define percentile

Answer 16

The value below which a percentage of data falls

Question 17

What is interpolation?

Answer 17

Technique to estimate the Q1-3 and percentiles

This assumes the data values are evenly distributed

Question 18

What is the equation for linear interpolation?

Answer 18

(Quartile - freq. below / freq of group) x width + lower class boundary

Question 19

What is the range?

Answer 19

Difference between largest and smallest values in the data set

Question 20

What is the interquartile range IQR?

Answer 20

Difference between upper and lower quartile

Q3 - Q1

Question 21

Why is IQR used?

Answer 21

It does not include extreme values

Only considers spread of middle 50% of the data

Question 22

What is the inter-percentile range?

Answer 22

Difference between the values for two given percentiles

Question 23

What is variance a measure of?

Answer 23

The spread of a data

Question 24

What is the equation for variance?

Answer 24

(Sum of x^2/n) - (Sum of x/n)^2

Question 25

What is the equation for standard deviation?

Answer 25

``` Sqrt of (Sum of x^2/n) - (Sum of x/n)^2 Square root of variance ```

Question 26

How is variance/standard dev. different for grouped data in a frequency table?

Answer 26

x is always times by its frequency

Question 27

What is coding?

Answer 27

A technique to simplify statistical calculations | Allows easier data to work with

Question 28

What is the equation for coding data?

Answer 28

y = (x-a)/b

Question 29

What is the equation for the mean of coded data?

Answer 29

mean of y = (mean of x - a)/b

Question 30

What is the standard dev. of coded data?

Answer 30

Coded standard dev. = standard dev. / b

Question 31

What affects measures of location and spread in coding?

Answer 31

Add/subtract affects mean not spread | All affected by stretch x or /

Question 32

What is the formula for sample variance?

Answer 32

Sum of (x - mean of x)^2 / (n-1)

Question 33

What is the formula for sample standard deviation?

Answer 33

Square root: Sum of (x - mean of x)^2 / (n-1)

Question 34

What are the advantages and disadvantages of range?

Answer 34

Adv: Easiest measure of dispersion to calculate Dis: Heavily affected by extreme values, no info on spread of the rest of the values

Question 35

What are the advantages and disadvantages of interquartile range?

Answer 35

Adv: Not affected by extreme values (used when outliers present) Dis: Difficult to calculate for grouped data

Question 36

What are the advantages and disadvantages of variance?

Answer 36

Adv: Depends on all data values Dis: Difficult to calculate, affected by outliers, different units from actual data values

Question 37

What are the advantages and disadvantages of standard deviation?

Answer 37

Adv: Depends on all data values, same units as data values Dis: difficult to calculate, affected by outliers