1 + 2

Question 1

Definition of statistical / mathematical model

Answer 1

Simplification of a real world situation.

Question 2

Advantages of model (5)

Answer 2

1. use to make predictions
2. by analysing, improve understanding of the real situation
3. help provide more control
4. quick + easy
5. simplify a more complex situation

Question 3

Disadvantages of model (2)

Answer 3

1. partial description of real situation

2. only work for restricted range of variables

Question 4

definition of qualitative data

Answer 4

data that cannot be measured numerically (uncountable)

Question 5

definition of discrete variable

Answer 5

a variable that can take only specific values in a given range (single values)

Question 6

definition of continuous variable

Answer 6

a variable that can take any value in a given range (measured a different accuracies)

Question 7

definition of quantitative data

Answer 7

data that can be measured numerically (countable)

Question 8

equation for medium

frequency table, grouped data, discrete

Answer 8

frequency table= n + 1 / 2

grouped data (in classes) = n / 2 (+ use interpolation)

discrete = n / 2 (if not whole no, round up)

Question 9

equation for mean

Answer 9

sum of x / number of values

Question 10

equation for mean in frequency table

Answer 10

table headers: x / f / fx

mean = sum of fx / sum of f

Question 11

equation for mean in grouped data

Answer 11

table headers: class / f / x (mid point) / fx

mean = sum of fx / sum of f

Question 12

how to combine means

you know mean and no of values for each

Answer 12

mean = sum of x / no of values
sum of x = mean x no of values
add both ‘sum of x’ together
work out mean= total ‘sum of x’ / total no of values

Question 13

what is interpolation used for

Answer 13

more specific medium in grouped data

Question 14

there is grouped data: 
class   / f / cf
30-31 / 2 / 2
32-33 / 25 / 27
34-36 / 30 / 57

you figured out medium (n / 2) and now you know the medium term.

Interpolate

Answer 14

1. 35th is between 27-57
   find fraction 35th term is between 27-57:
   35 - 27 / 57 -27 (remember smallest goes last)
   = 8 / 30

3. 27-57 is in class 34-36
find class boundaries 
you have class 34-36
so is 33.5-36.5
difference of 3 

4. so medium is 8 / 30 x 3 = 8 / 10
5. don’t forget to add lower boundary: 33.5
   so 33.5 + 8 /10 = 34.3 mm

Question 15

what is usually coding used for

Answer 15

mean and makes large numbers easier to work with

Question 16

on grouped data, how do you find the mean with coding involved:

class / f / x (which is the mid point) / code / fy

Answer 16

mean of coded data = sum of fy / sum of f

+ rearrange the code given so x is the subject + add values in (value of mean of coded data given above)

Question 17

what is x in grouped data

Answer 17

THE MID POINT

Question 18

mean of coded data

Answer 18

sum of fy / sum of f

Question 19

if there is no gaps in grouping

Answer 19

NO UPPER AND LOWER BOUNDARIES

Question 20

If given a mean and one person gave wrong ‘x’ or answer, if the new ‘x’ is higher what will happen to mean

Answer 20

Higher mean

Question 21

If given a mean and one person gave wrong ‘x’ or answer, if the new ‘x’ is lower what will happen to mean

Answer 21

lower mean

Question 22

If given a mean and one person gave wrong ‘x’ or answer, figure out new mean

Answer 22

mean = sum of x / n

figure of old sum of x by mean x n
add or subtract the difference of new ‘x’ and old ‘x’
redo calculate new mean

Question 23

you get a mean for 50 days, then a mean for 90 days, they ask for a mean for the extra 40 days, how?

Answer 23

you find out the sum of x for the 50 days

you fill in the equation for the mean for 90 days:
mean = ‘sum of x for 50 days’ + x / 90

rearrange to find out x

this x is your sum of x for the extra 40 days
fill in the equation for the mean for 40 days