Statistics Chapter 2

Question 1

What is a measure of location?

Answer 1

A single value describing a position in a data set

Question 2

What is a measure of central tendency?

Answer 2

A single value describing the centre of a data set

Question 3

What is the mode/modal class?

Answer 3

The most often occurring value or class

Question 4

What is the median?

Answer 4

The middle value of an ordered set of data

Question 5

What is the mean?

Answer 5

The sum of the data values divided by the number of data values
x bar = sum of x / n

Question 6

When should the mode be used? (2)

Answer 6

Qualitative data

Quantitative data with repeating values

Question 7

What is a data set with two modes called?

Answer 7

Bimodal

Question 8

When should the median be used?

Answer 8

Quantitative data; especially data with extreme values and outliers as they do not affect the average

Question 9

When should the mean be used?

Answer 9

Quantitative data as it uses all values in order to give a true measure; not suitable when there are extreme values as this has a big effect on the average

Question 10

What is the four pots method used for?

Answer 10

Finding quantiles for discrete data

Question 11

How does the four pots method work? (3)

Answer 11

Divide the number of pieces of data by four
Place the data values as equally as possible into the four pots
Add remainders as evenly as possible in the spaces between the pots

Question 12

What is linear interpolation used for?

Answer 12

Finding quartiles for continuous data

Question 13

What is a measure of spread?

Answer 13

A measure of how spread out the data is

Question 14

What is the range? (2)

Answer 14

The difference between the largest and smallest data values

Affected by extreme values

Question 15

What is the interquartile range? (2)

Answer 15

Difference between quartile 1 and quartile 3

Not affected by extreme values but only considers middle 50%

Question 16

What is the interpercentile range? (2)

Answer 16

Difference between two given percentiles

Often uses 10% and 90% as this gives a measure from 80% of the data but discounts extreme values

Question 17

What is variance?

Answer 17

Works out the spread of the data

Question 18

How is variance calculated? (2)

Answer 18

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

Sxx / n

Question 19

What is standard deviation? (2)

Answer 19

The higher the number the more spread out the data is

Always positive

Question 20

How is standard deviation calculated?

Answer 20

✔️(sum of x^2 / n) - (x bar)^2

Question 21

How is the standard deviation of grouped data calculated? (2)

Answer 21

✔️(sum of fx^2 / sum of f) - (sum of fx / sum of f)^2

Where x = midpoints of each group

Question 22

What is coding?

Answer 22

A set of data values can be modified by using a formula:

y = (x - a) / b

Question 23

How is the mean of coded data converted to the mean of the original data? (2)

Answer 23

(y bar) = (x bar) - a / b

Mean is affected by all transformations so it must be divided and subtracted from

Question 24

How is the standard deviation of coded data converted to the standard deviation of the original data? (2)

Answer 24

(sigma y) = (sigma x) / b

As standard deviation is a measure of spread, adding or subtracting has no effect