Numerical Measures and Data Representation

Question 1

How to work out the Mean [x̄]

Answer 1

Sum of data values / number of data values

x̄ = Σx / n

Question 2

How do you work out the mean[x̄] from a frequency table?

Answer 2

Add new column that multiplies number (if needed do midpoint) by frequencies = (n*f)

x̄ = Σ(n*f) / Σf

Question 3

Q1 =

Answer 3

lower quartile

for grouped data
= 1/4 nth data value

for non-grouped data
= (n+1)/4

Question 4

Q2 =

Answer 4

Median

for grouped data
= 1/2 nth data value

for non-grouped data
= (n+1)/2

Question 5

Q3

Answer 5

Upper Quartile

for grouped data
= 3/4 nth data value

for non-grouped data
= ((n+1)/4) *3

Question 6

In Listed Data - for quartiles - if a decimal…

Answer 6

round up !

Question 7

In Listed data - for quartiles - if whole…

Answer 7

find midpoint with the next one

Question 8

For finding Quartiles in Grouped data:

Answer 8

INTERPOLATION

Question 9

What is Variance?

Answer 9

Shows how spread out data is.
(σ2)

Question 10

Standard Deviation (σ) fb

Answer 10

root of variance.

σ = √(Σx2/n) - (Σx/n)2
{mean of squares minus square of means}

Question 11

Standard Deviation/ Variance form a frequency table

Answer 11

USE CALCULATOR
- menu
- 6:Statistics
-1: 1-variable
- Fill Table (using Midpoints)
- Option
- 3: 1-variable Calc

Question 12

For coded data what terms affect the Standard Deviation?

Answer 12

only terms multiplied or divided

Question 13

Histogram how do you calculate Frequency Density ?

Answer 13

frequency / class width

Question 14

How do you draw a boxplot from a cumulative frequency diagram?

Answer 14

Find median in CumFreq and trace down to x-axis to get the data correlation
Half median to get LQ and add LQ to Median to get UQ then again map to x-axis to get actual data for each

Top value is most extreme value MAXIMUM
and Bottom value is least extreme value on the boxplot MINIMUM

Question 15

Why use a histogram?

Answer 15

data is continuous
no gaps

Question 16

Comparing two diagrams what should you talk about?

Answer 16

1. Location
2. Spread

Question 17

What is the range for ‘r’ in Product Moment Correlation Coefficient?

Answer 17

-1<= r <= 1
PMCC measures strength and positivity of correlation - this is why can only go between 1 and -1

Question 18

Regression line

Answer 18

Line of Best Fit
y = a + bx

Question 19

What is meant by the term Interpolation?

Answer 19

Estimating inside the data range

Question 20

What is meant by Extrapolation?

Answer 20

estimating outside the data range

Question 21

When do you change boundaries in grouped data?

Answer 21

when there is a gap and it is continuous data

use these new boundaries to find midpoints

Question 22

Frequency Diagram

Answer 22

(x,y) <- plot points
x=upper class boundary
y=cumulative frequency

join with a curve

Question 23

frequency polygon

Answer 23

(x,y)
x= midpoint
y=frequency density

join up with straight lines

Question 23

Area of bar [histogram]

Answer 23

PROPORTIONAL to frequency
(if not to scale find scale factor)
always check scale on histogram

Question 23

What are histograms used for?

Answer 23

grouped, continuous data

Question 24

Pros and Cons of Box Plot

Answer 24

+ highlights outliers
+easy to compare data sets

-data categorised in 4 sections means detailed analysis is not possible

Question 25

Pros and Cons Histogram

Answer 25

+clearly shows shape of distribution

• doesnt always highlight outliers
• not easy to estimate quartiles and median

Question 26

Cumulative Frequency Curve Pros and Cons

Answer 26

+ makes it easy to find the min, LQ, median, UQ and max

• doesnt always highlight outliers