INTERMEDIATE 2 – ADDITIONAL QUESTION BANK UNIT 2 : Statistics You have chosen to study: Please...

INTERMEDIATE 2 – ADDITIONAL QUESTION BANK

UNIT 2 :Statistics

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STATISTICS : Question 1

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A taxi company was phoned each night of the week and the response time in minutes of their cars were noted. They were ….

3 5 10 7 7 15 9

(a) Find the mean and standard deviation for this data.

(b) A similar experiment was conducted with a second company. The results for this were….

mean = 12 and standard deviation = 1.88

How does the second company compare to the first?

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3 5 10 7 7 15 9





nmean

n

Draw a table comparing data

to mean.Then square

values.

2

1

x xSD

n

When comparing data sets always

make comment on the average (which is bigger etc.) and the spread of the data.

What would you like to do now?

(b)The second company has a longer average response time. The smaller standard deviation means their arrival time is more predictable.


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3 5 10 7 7 15 9





(a) Mean = 8 3.87SD


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3 5 10 7 7 15 9


(a)

Mean = (3+5+10+7+7+15+9)7 = 8

1. Calculate mean.

So = 8

and no.pieces of data = n = 7

x

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3 5 10 7 7 15 9


2. Draw table comparing data to mean.

x

3 -5 25

5 -3 9

10 2 4

7 - 1 1

7 -1 1

15 7 49

9 1 1

(x - )2 = 90x

8x

x x 2x x

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3 5 10 7 7 15 9


3. Use formula to calculate standard deviation.

2

1

x xSD

n

90

6SD

3.87SD

Just found!!

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Question 1

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1. Always compare mean and standard deviation.(b) A similar experiment was

conducted with a second company. The results for this were….



(b)The second company has a

longer average response time.

The smaller standard deviation means their arrival time is more

predictable.

8x 3.87SD What would you like to do now?

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3. Use formula to calculate standard deviation.

2

1

x xSD

n

90

6SD

3.87SD

Check the list of Formulae for the Standard Deviation Formula:

The second formula can be used in the calculator paper.The calculator must be in Stats. Mode to allow the data to be entered.

22

2( )

x( ) or

1 1

xx x nn n


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Weeks of training

Tim

e(s

)

A TV personality takes part in a 20 week training schedule to copy a 100m sprinter. Her times are recorded every 2 weeks and plotted in the graph then a line of best fit is drawn.

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Weeks of training

Tim

e(s

)

(i) Find the equation of the line in terms of T and W.

(ii) Use answer (i) to predict (a) her time after 12 weeks of training

(b) the week when her time was 11.5secs




Use your equation and substitute W = 12.


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Weeks of training

Tim

e(s

) Find gradient and

note intercept of T axis.

Use your equation and substitute T = 11.5



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Weeks of training

Tim

e(s

)




T = -¼ W + 15

12secs.

14 weeks


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1. Find gradient and note intercept of T axis.


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m = (y2 – y1)(x2 – x1)

(a) 10 - 15 20 - 0

=

Intercept at 15

Equation is T = -¼ W + 15

= -¼

(ii) Use answer (i) to predict

(a) her time after 12 weeks of training


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2. Use your equation and substitute

W = 12.

(b)(i) If w = 12 then T = -¼ W + 15

becomes T = (-¼ x 12) + 15= -3 + 15

= 12

Time at 12 weeks is 12secs.

(ii) Use answer (i) to predict

(a) her time after 12 weeks of training


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3. Use your equation and substitute

T = 11.5

(b)(i) If t = 11.5 then T = -¼ W + 15

becomes -¼ W + 15 = 11.5(-15) (-15)

-¼ W = -3.5 x (–4)

W = 14

Reach a time of 11.5sec after 14 weeks.


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m = (y2 – y1)(x2 – x1)

(a) 10 - 15 20 - 0

=

Intercept at 15


= -¼

To find the equation of a line from the graph:

Must Learn:

y = mx + c

gradient intercept

So you need to find these!!

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m = (y2 – y1)(x2 – x1)

(a) 10 - 15 20 - 0

=

Intercept at 15


= -¼

m = verticalhorizontal

Note: Always draw the horizontal before the vertical:

horizontal (+ve)

vertical (-ve)

(a) What percentage liked Shrek but not the Simpsons?

(b) If someone is picked at random what is the probability that

(i) they liked the Simpsons but not Shrek?

(ii) they liked neither?


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A sample of 180 teenagers were asked their opinions on the TV series the “Simpsons” & the movie “Shrek” and their responses were displayed in the following table… Like

Simpsons

Like Shrek

Don’t like Simpsons

Don’t like Shrek

126

2115

?






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Simpsons

Like Shrek


Don’t like Shrek

126

2115

?

Remember all entries in table must add to total sample size

To find probabilities use:

P = no of favourable / no of data







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Simpsons

Like Shrek


Don’t like Shrek

126

2115

?

10%

1/12

7/60

What now?

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1. Use P = no of favourable / no of dataLike Simpsons

Like Shrek


Don’t like Shrek

126

2115

?

(a)What percentage liked Shrek but not the Simpsons?

(a) Like Shrek but not Simpsons

= 180 – 126 – 15 – 21

= 18

% = 18/180 = 1/10 = 10%

NB: There are 180 in survey!!

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Like Shrek


Don’t like Shrek

126

2115

?

what is the probability that(i) they liked the Simpsons but not Shrek?

(b)(i) Prob = 15/180 = 1/12

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Like Shrek


Don’t like Shrek

126

2115

?


(b)(ii) Prob = 21/180 = 7/60


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1. Use P = no of favourable / no of data

(a) Like Shrek but not Simpsons

= 180 – 126 – 15 – 21

= 18

% = 18/180 = 1/10 = 10%

NB: There are 180 in survey!!

Note: To change a fraction to a % multiply by 100%

18180

= x 100% 18180

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1. Use P = no of favourable / no of data

(b)(i) Prob = 15/180 = 1/12

Probability =

Number of favourable outcomes Number of possible outcomes

To calculate simple probabilities:

(b) If a combination is selected at random what is the probability that it is ……


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On a college course you have to pick a language plus a

leisure activity from the following lists

LANGUAGE

FRENCH

GERMAN

SPANISH

LEISURE

MUSIC

VIDEO PRODUCTION

BASKETBALL

SWIMMING

(a) Make a list of all possible combinations of courses.

(i) Includes Spanish?

(ii) Includes swimming?

(iii) Doesn’t include French but includes music?



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LANGUAGE

FRENCH

GERMAN

SPANISH

LEISURE

MUSIC

VIDEO PRODUCTION

BASKETBALL

SWIMMING





Use a tree diagram & “branch out” with

each language.

From each language “branch

out” with each leisure activity.

Now list the pairs

of subjects.

Use your list of possible

combinations to find probabilities.




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LANGUAGE

FRENCH

GERMAN

SPANISH

LEISURE

MUSIC

VIDEO PRODUCTION

BASKETBALL

SWIMMING





1/3

1/4 1/6

CLICK

GERMAN

FRENCH

SPANISH

BASKETBALL

VIDEO

MUSIC

SWIMMING

BASKETBALL

VIDEO

MUSIC

SWIMMING

BASKETBALL

VIDEO

MUSIC

SWIMMING

(a)French/Music

French/Video

French/Bsktbll

French/Swim

German/Music

German/Video

German/Bsktbll

German/Swim

Spanish/Music

Spanish/Video

Spanish/Bsktbll

Spanish/Swim

Hints

Use a tree diagram & “branch out” with each language.

From each language “branch out” with each leisure activity.

Now list the pairs of subjects.

Hints

Have list of combinations handy.

Remember to simplify.

French/Music

French/Video

French/Bsktbll

French/Swim

German/Music

German/Video

German/Bsktbll

German/Swim

Spanish/Music

Spanish/Video

Spanish/Bsktbll

Spanish/Swim

= 1/3

= 1/4

(b)(i) Prob

(b)(ii) Prob

= 4/12

= 3/12

(b)(iii) Prob = 2/12 = 1/6

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(iii)Doesn’t include French

but includes music?

What is probability:

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GERMAN

FRENCH

SPANISH

BASKETBALL

VIDEO

MUSIC

SWIMMING

BASKETBALL

VIDEO

MUSIC

SWIMMING

BASKETBALL

VIDEO

MUSIC

SWIMMING

(a)French/Music

French/Video

French/Bsktbll

French/Swim

German/Music

German/Video

German/Bsktbll

German/Swim

Spanish/Music

Spanish/Video

Spanish/Bsktbll

Spanish/Swim

No. of possible outcomes

= 3 x 4 = 12

Probability =

Number of favourableNumber of possible

To calculate simple probabilities:

The delivery times for a fast food company are shown in the following cumulative frequency table.

Time No. Deliveries

up to 4 mins 5

up to 8 mins 13

up to 12 mins 37

up to 16 mins 53

up to 20 mins 60

(b) Use the data to construct a cumulative frequency graph.

(c) Use the graph to find the median and semi-interquartile range for this data.

(a) How many deliveries took longer than 16 mins?


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Time No. Deliveries

up to 4 mins 5

up to 8 mins 13

up to 12 mins 37

up to 16 mins 53

up to 20 mins 60





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For how many greater than

16 find difference

between end value of

values up to 16.

Median is middle

value- so we want

halfway-point on

frequency axis.

SIQR = ½(Q3 – Q1)

Q1 – 25% point & Q3 – 75% point



Time No. Deliveries

up to 4 mins 5

up to 8 mins 13

up to 12 mins 37

up to 16 mins 53

up to 20 mins 60





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= 7

Median = 11 mins SIQR = 2.75 mins

Delivery time(mins)

Cum freq

Q2

11

Q1

8.5

Q3

14

½ of 60 = 30

¼ of 60 = 15

¾ of 60 = 45

(C) Median = 11mins. (c) SIQR = ½(Q3 – Q1) = (14 – 8.5) 2 = 2.75mins

(a) Deliveries taking longer than 16 mins = 60 – 53 = 7

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Time Deliveries

4 5

8 13

12 37

16 53

20 60What would you like to do now?

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Cumulative Frequency

DeliveryTime

60

20

50%

11

Note: In a Cumulative Frequency Diagram:

On y-axis (cumulative frequency)

Q1 at 25%, Q2 at 50%,

Q3 at 75%

And read values from the delivery time scale (x-axis).

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INTERMEDIATE 2 – ADDITIONAL QUESTION BANK UNIT 2 : Statistics You have chosen to study: Please...

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