## Representing Data

## Types of Data

**Qualitative Data**

- Eye Colour
- Blood Group
- Gender

**Quantitative Data**

- Numeric Values

**Continuous Data**

Data that can take any value within a given range

- Height
- Weight
- Time

**Discrete Data**

Data that has distinct and separate values

- Lottery numbers
- Amount of Money
- Number of TV episodes

## Representing Data

**Data Line**

E.g. 10, 20, 20, 20, 23, 25, 30, 31, 54

n = 9

What you did at GCSE

**Mode**= 20

**Mean**=

**= 25.89 2 d.p.**

__Σ____x__**n**

**Median (Q2)**= 23

Q2 position =

__n__= 4.5 so 5th position

2 count to 5th position which is 23

**Frequency Table**

E.g.

**Mode**= 0

**Mean =**=

__Σfx____49__= 1.53 2 d.p.

**Σf**32

**Median**= 1.5

Q2 position = 32/2 = 16 want in between 16th and 17th - median means 50% data on either side

Use cumulative frequency and 16 and 17 are in different x values so:

__1 + 2__= 1.5

2

**Grouped Frequency Table**

E.g. beware of difference in discrete and continuous data here

**Mode**= 21-30

**Mean =**=

__Σfx____2017.5__= 30.1 3 s.f.

**Σf**67

**Median**is done via

**linear interpolation**explained lower

**Mode**= 50-79

**Mean =**=

__Σfx____3912__= 58.4 3 s.f.

**Σf**67

**Median**is done via

**linear interpolation**explained lower

## Linear Interpolation

In grouped data there is no way of telling what the median value is exactly . And as there isn't a data line we can't tell exactly. Linear interpolation provides a best guess at the median

Frequency of group

__Class width x (Q2 pos - previous cumulative freq)__+ LBFrequency of group

**Q2 position = 34th position**

27

__30 x (34 - 24)__+ 49.5 = 60.61 2 d.p.27

## Coding

Coding enables large numbers to be simplified

When working oiut means with coded data. This is the y value - put this equal to the code equation and you get the real mean

E.g.

y = x -100

mean of coded is 30

30 = x -100

x = 130

mean = 130

**y =****where a and b are constants and y is the coded value and x is the original value**

__x - a__

bWhen working oiut means with coded data. This is the y value - put this equal to the code equation and you get the real mean

E.g.

y = x -100

mean of coded is 30

30 = x -100

x = 130

mean = 130