Statistics- Measures of location and spread (2)

Question 1

Mode/ modal class

Answer 1

Value or class that occurs most often

Question 2

Median

Answer 2

Middle value when the data values are put in order

Question 3

Mean

Answer 3

Average of values

x̄ = Σx / n

Question 4

Mean (frequency table)

Answer 4

x̄ = Σxf / Σf
x = midpoint of each class interval

Question 5

Use mode if:

Answer 5

Data is qualitative or if quantitative data has a single mode

Question 6

Use median if:

Answer 6

Data is quantitative and there are outliers

Question 7

Use mean if:

Answer 7

Data is quantitative and no outliers.

Question 8

Lower quartile (Q₁)

Answer 8

One-quarter of way through data set

Question 9

Upper quartile (Q₃)

Answer 9

Three-quarters of the way through the data set

Question 10

Percentiles

Answer 10

Splits data set into 100 parts

Question 11

Interpolation

Answer 11

Used when data is presented in a grouped frequency table to estimate the median, quartiles and percentiles
-assumes data values are evenly distributed

Question 12

Range

Answer 12

largest value- the smallest value

Question 13

IQR

Answer 13

Q₃ - Q₁

Question 14

Inter-percentile range

Answer 14

Difference between the values for two given percentiles

Question 15

Variance

Answer 15

σ² = Σ(x - x̄)² / n
σ² = (Σx² / n) - (Σx/n)²
σ² = Sₓₓ / n
‘the mean of the squares minus the square of the mean’

Question 16

Summary statistic

Answer 16

Sₓₓ = Σ(x - x̄)²
Sₓₓ = Σx² - (Σx)² / n

Question 17

Standard deviation

Answer 17

Square root of the variance
σ = √(Σ(x - x̄)² / n)
σ = √((Σx² / n) - (Σx/n)²)
σ = √(Sₓₓ / n)

Question 18

Standard deviation (frequency table)

Answer 18

σ = √(Σf(x - x̄)² / Σf) = √((Σfx² / Σf) - (Σfx / Σf)²)

Question 19

Coding

Answer 19

A way of simplifying statistical calculations. Each data value is coded to make a new set of values which are easier to work with

Question 20

Coding formula

Answer 20

y = (x - a) / b
mean : ȳ = (x̄ - a) / b
standard deviiation: σᵧ = σₓ / b
σₓ is the standard deviation of the original data