Sec 2 · G1 (N(T))

Statistics

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1. Dot diagrams, stem-and-leaf diagrams and histograms

A dot diagram of books read (3, 4, 4, 5, 5, 5, 6, 6, 7, 9), and a histogram of times in classes of 10 minutes with frequencies 3, 7, 12, 6 and 2, bars touching.

Stem	Leaf
$2$	$3\ 5\ 8$
$3$	$0\ 4\ 4\ 7$
$4$	$1\ 6$
Key: $3 \mid 4$ means $34$

📖 Worked example

The dot diagram shows the number of hours some pupils slept last night. Find the median.

Step 1 of 2

Count the dots: each dot is one value

Number of values

= 14

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2. Mean, median and mode

Average	Meaning	Books read: $3, 4, 4, 5, 5, 5, 6, 6, 7, 9$
mean	$\dfrac{\text{sum}}{\text{number of values}}$	$\dfrac{54}{10}$ , so $5.4$
median	the middle value, in order	the 5th and 6th are both $5$ : $5$
mode	the most common value	$5$

Mean from a frequency table: Σfx ÷ Σf

\displaystyle \dfrac{1(2) + 2(5) + 3(3)}{2 + 5 + 3}

e.g.

\displaystyle \dfrac{1(2) + 2(5) + 3(3)}{2 + 5 + 3}

\displaystyle = 2.1

📖 Worked example

The numbers of books read by 6 pupils last month are $3,\ 0,\ 8,\ 4,\ x,\ 1$ . The mean is $3$ . Find $x$ .

Step 1 of 3

Total of all the values = mean × number of values

Total

= 3 \times 6

= 18

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3. Histograms

To find	On the histogram
the frequency of a class	the height of its bar
the total frequency	add the heights of all the bars
the modal class	the class of the tallest bar
how many have $t > 30$	add the bars to the right of $30$

📖 Worked example

The histogram shows the distances, $d$ km, that the members of a cycling club rode last Sunday. Find the number of members with $d > 30$ .

Step 1 of 2

Values more than 30: the classes from the boundary 30 upwards

d > 30

: the classes

30 < d \le 40

60 < d \le 70

(a value of exactly

30

is in the class below).

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4. Choosing a statistical diagram

Diagram	Best for	Limitation
Dot diagram	a small set of data with a few different values	too crowded for a large set of data
Stem-and-leaf diagram	keeping every value while showing the shape; the median is easy to find	needs a key; awkward for a very large set

Diagram	Best for	Limitation
Histogram	a large set of continuous data grouped in equal classes (bars touch)	the original values are lost

📖 Worked example

The marks out of 100 of 25 pupils in a test (from 31 to 98) are to be shown so that every mark is kept and the median is easy to find. Which statistical diagram is the most suitable?

Step 1 of 2

What must the diagram do?

The diagram has to keep every value while showing the shape of the data.

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Sec 2 · G1 (N(T))

Statistics

Practise statistics with step-by-step help. Free account.

Start free

1. Dot diagrams, stem-and-leaf diagrams and histograms

Stem	Leaf
$2$	$3\ 5\ 8$
$3$	$0\ 4\ 4\ 7$
$4$	$1\ 6$
Key: $3 \mid 4$ means $34$

📖 Worked example

The dot diagram shows the number of hours some pupils slept last night. Find the median.

Step 1 of 2

Count the dots: each dot is one value

Number of values

= 14

Practise this →

2. Mean, median and mode

Average	Meaning	Books read: $3, 4, 4, 5, 5, 5, 6, 6, 7, 9$
mean	$\dfrac{\text{sum}}{\text{number of values}}$	$\dfrac{54}{10}$ , so $5.4$
median	the middle value, in order	the 5th and 6th are both $5$ : $5$
mode	the most common value	$5$

Mean from a frequency table: Σfx ÷ Σf

\displaystyle \dfrac{1(2) + 2(5) + 3(3)}{2 + 5 + 3}

e.g.

\displaystyle \dfrac{1(2) + 2(5) + 3(3)}{2 + 5 + 3}

\displaystyle = 2.1

📖 Worked example

The numbers of books read by 6 pupils last month are $3,\ 0,\ 8,\ 4,\ x,\ 1$ . The mean is $3$ . Find $x$ .

Step 1 of 3

Total of all the values = mean × number of values

Total

= 3 \times 6

= 18

Practise this →

3. Histograms

To find	On the histogram
the frequency of a class	the height of its bar
the total frequency	add the heights of all the bars
the modal class	the class of the tallest bar
how many have $t > 30$	add the bars to the right of $30$

📖 Worked example

The histogram shows the distances, $d$ km, that the members of a cycling club rode last Sunday. Find the number of members with $d > 30$ .

Step 1 of 2

Values more than 30: the classes from the boundary 30 upwards

d > 30

: the classes

30 < d \le 40

60 < d \le 70

(a value of exactly

30

is in the class below).

Practise this →

4. Choosing a statistical diagram

Diagram	Best for	Limitation
Dot diagram	a small set of data with a few different values	too crowded for a large set of data
Stem-and-leaf diagram	keeping every value while showing the shape; the median is easy to find	needs a key; awkward for a very large set

Diagram	Best for	Limitation
Histogram	a large set of continuous data grouped in equal classes (bars touch)	the original values are lost

📖 Worked example

The marks out of 100 of 25 pupils in a test (from 31 to 98) are to be shown so that every mark is kept and the median is easy to find. Which statistical diagram is the most suitable?

Step 1 of 2

What must the diagram do?

The diagram has to keep every value while showing the shape of the data.

Practise this →

Practise statistics with step-by-step help

Endless questions from basic to exam level. Get one wrong and see where it went wrong. Free account.

Start free