Figure — understand the maths, don't just answer it

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

Types of data and grouped frequency

6 questions

LessonNot started

State whether each of the following variables is qualitative or quantitative, and if quantitative, whether it is discrete or continuous:
(a) the number of goals scored in a football match;
(b) the time taken to complete a puzzle;
(c) a person's eye colour.

●●●●●Level 23 marksStart

A student records the mass of each of

30

apples. State whether this data is discrete or continuous, and explain your answer.

●●●●●Level 22 marksStart

Measures of location — mean, median, mode and quartiles

33 questions

LessonNot started

The number of times,

x

, that each of

50

households used a recycling centre in a month is summarised below.

\begin{array}{|c|c|c|c|c|c|}\hline x & 0 & 1 & 2 & 3 & 4 \\ \hline \text{Frequency} & 5 & 12 & 18 & 9 & 6 \\ \hline\end{array}

Find the mean and the standard deviation of

x

. (4 marks)

●●●●●Level 24 marksStart

A radio station records the length,

x

seconds, of each of the 40 advertisements that it broadcasts one morning.

The lengths are coded using

y = \frac{x - 30}{5}

and the coded data are summarised by

\sum y = 26 \qquad \sum y^2 = 212

(a) Find the mean of

x

(2 marks)
(b) Find the standard deviation of

x

(3 marks)

The station manager converts each length into minutes.
(c) Find the mean and the standard deviation of the lengths in minutes.

(2 marks)

●●●●●Level 27 marksStart

Find the mean of the data

12, 15, 11, 18, 14

.

●●●●●Level 22 marksStart

Find the median of the data

7, 3, 9, 5, 11, 8

.

●●●●●Level 22 marksStart

Measures of spread, standard deviation and coding

38 questions

LessonNot started

The number of times,

x

, that each of

50

households used a recycling centre in a month is summarised below.

\begin{array}{|c|c|c|c|c|c|}\hline x & 0 & 1 & 2 & 3 & 4 \\ \hline \text{Frequency} & 5 & 12 & 18 & 9 & 6 \\ \hline\end{array}

Find the mean and the standard deviation of

x

. (4 marks)

●●●●●Level 24 marksStart

A radio station records the length,

x

seconds, of each of the 40 advertisements that it broadcasts one morning.

The lengths are coded using

y = \frac{x - 30}{5}

and the coded data are summarised by

\sum y = 26 \qquad \sum y^2 = 212

(a) Find the mean of

x

(2 marks)
(b) Find the standard deviation of

x

(3 marks)

The station manager converts each length into minutes.
(c) Find the mean and the standard deviation of the lengths in minutes.

(2 marks)

●●●●●Level 27 marksStart

A data set has smallest value

5

, largest value

30

, lower quartile

12

and upper quartile

20

. Find the range and the interquartile range.

●●●●●Level 22 marksStart

Histograms and frequency polygons

15 questions

LessonNot started

The histogram shows information about the lengths of time, in minutes, that 160 visitors spent in an art gallery on one day.It is given that 30 visitors spent between 10 and 20 minutes in the gallery.
(a) Find the number of visitors who spent between 40 and 80 minutes in the gallery.

(1 mark)
(b) State the units of the frequency density.

(1 mark)
(c) Suggest one change that the gallery could make to the diagram so that it would provide more information.

(1 mark)
(d) Estimate the number of visitors who spent between 60 and 80 minutes in the gallery.

(1 mark)

●●●●●Level 24 marksStart

Correlation and regression

18 questions

LessonNot started

Bea is studying how the depth of snow on a mountain path changes during the spring.

She measures the depth of snow,

d

cm, at time

t

days after 1 March, for each of the

15

days from

t = 0

to

t = 14

Bea finds the equation of the regression line of

d

on

t

for her data to be

d = 62.4 - 3.15t

(a) Interpret the gradient of this line.

(1 mark)
(b) Interpret the value

62.4

in Bea's model.

(1 mark)

Bea uses her regression line to estimate the depth of snow on the path when

t = 40

(c) Give a reason why this estimate may not be reliable.

(1 mark)

●●●●●Level 23 marksStart

Exponential models and regression

17 questions

LessonNot started

The regression line of

\log_{10} y

on

x

is

\log_{10} y = 0.3 + 0.2x

. Express

y

in terms of

x

, giving the constants to 3 significant figures.

●●●●●Level 22 marksStart

Using the model

\log_{10} y = 0.3 + 0.2x

, estimate the value of

y

when

x = 5

.

●●●●●Level 22 marksStart

The regression line of

\log_{10} y

on

x

is

\log_{10} y = 0.5 + 0.3x

.

Express the model in the form

y = ab^{x}

, giving

a

and

b

to 3 significant figures. (3 marks)

●●●●●Level 23 marksStart

Measuring correlation (the PMCC)

29 questions

LessonNot started

For a set of bivariate data,

S_{xy} = 100

,

S_{xx} = 72

and

S_{yy} = 152

. Find the product moment correlation coefficient

r

, to 3 decimal places.

●●●●●Level 22 marksStart

For a set of bivariate data,

S_{xy} = 60

,

S_{xx} = 90

and

S_{yy} = 160

.

Calculate the product moment correlation coefficient. (2 marks)

●●●●●Level 22 marksStart

For each of the following, describe the correlation and suggest what it means in context.
(a) Hours of revision and exam mark:

r = 0.92

. (2 marks)
(b) Shoe size and reaction time:

r = -0.15

. (1 mark)

●●●●●Level 23 marksStart