Statistics Toolkit

There are 18 packets of sweets and 12 boxes of sweets in a carton.

The mean number of sweets in all the 30 packets and boxes is 14.
The mean number of sweets in the 18 packets is 10.

Work out the mean number of sweets in the boxes.

There are 15 children at a birthday party.

The mean age of the 15 children is 7 years.

9 of the 15 children are boys.
The mean age of the boys is 5 years.

Work out the mean age of the girls.

There are 10 boys and 20 girls in a class.
The class has a test.

The mean mark for all the class is 60
The mean mark for the girls is 54

Work out the mean mark for the boys.

Walkden Reds is a basketball team.

At the end of 11 games, their mean score was 33 points per game.
At the end of 10 games, their mean score was 2 points higher.

Jordan says,

   "Walkden Reds must have scored 13 points in their 11th game."

Is Jordan right?
You must show how you get your answer.

Mr Brown gives his class a test.
The 10 girls in the class get a mean mark of 70%
The 15 boys in the class get a mean mark of 80%

Nick says that because the mean of 70 and 80 is 75 then the mean mark for the whole class in the test is 75%

Nick is not correct.
Is the correct mean mark less than or greater than 75%?
You must justify your answer.

Bob asked each of friends how many minutes they took to get to work.
The table shows some information about his results.

Time taken (m minutes)	Frequency

Work out an estimate for the mean time taken.

Sumeet records the times, in minutes, for 40 runners to finish a half marathon.
Information about these times is shown in the table.

Time ( minutes)	Frequency

Calculate an estimate for the mean time.

The table gives information about the heights of trees.

Height(  metres)	Frequency

Work out an estimate for the mean height of the trees.

The table gives information about the heights of girls.

Height( metres)	Frequency

Find the class interval that contains the median.

Work out an estimate for the mean height.

The table shows information about the weekly earnings of people who work in a shop.

Weekly earnings()	Frequency

Work out an estimate for the mean of the weekly earnings.

Nadiya says,

   "The mean may not be the best average to use to represent this information."

Do you agree with Nadiya?
You must justify your answer.

The table shows some information about the foot lengths of adults.

Foot length( cm)	Number of adults

Write down the modal class interval.

Calculate an estimate for the mean foot length.

Jenny works in a shop that sells belts.

The table shows information about the waist sizes of customers who bought belts from the shop in May.

Belt size	Waist(  inches)	Frequency
Small
Medium
Large
Extra Large

Calculate an estimate for the mean waist size.

Belts are made in sizes Small, Medium, Large and Extra Large.

Jenny needs to order more belts in June.
The modal size of belts sold is Small.

Jenny is going to order of the belts in size Small.
The manager of the shop tells Jenny she should not order so many Small belts.

Who is correct, Jenny or the manager?
You must give a reason for your answer.

Hannah is planning a day trip for 195 students.

She asks a sample of 30 students where they want to go.
Each student chooses one place.

The table shows information about her results.

25 students in class A did a science exam.
30 students in class B did the same science exam.

The mean mark for the 25 students in class A is 67.8
The mean mark for all the 55 students is 72.0

Work out the mean mark for the students in class B.                                           

Here are two sets of numbers, A and B.

mean of Set A : mean of Set B = 3 : 8

Work out the value of

The table shows some information about the dress sizes of women.

Dress size	Number of women

Find the median dress size.

of the  women have a shoe size of 
Zoe says that if you choose at random one of the  women, the probability that she has
either a shoe size of or a dress size of is  because

Is Zoe correct?
You must give a reason for your answer.

The time-series graph gives some information about the number of pairs of shoes sold in a shoe shop in the first six months of 2014.

The sales target for the first six months of 2014 was to sell a mean of 96 pairs of shoes per month.

Did the shoe shop meet this sales target?
You must show how you get your answer.

A bus company recorded the ages, in years, of the people on coach A and the people on coach B.

Here are the ages of the 23 people on coach A.

Complete the table below to show information about the ages of the people on
coach A.

Here is some information about the ages of the people on coach B.

Richard says that the people on coach A are younger than the people on coach B.

Is Richard correct?
You must give a reason for your answer.

Richard says that the people on coach A vary more in age than the people on coach B.

Is Richard correct?
You must give a reason for your answer.

The police record the speed of vehicles passing a speed checkpoint.
The speeds are recorded in the table below.

Speed (s mph)	Number of vehicles
	5
	8
	37
	47
	3

..................... mph [4]

[1]

A shop records the time taken by its customers to complete a purchase on its website.
The results from one day are summarised in this table.

Time taken ( minutes)	Number of customers
	6
	10
	6
	2
	1

Calculate an estimate of the mean time taken.

....................... minutes

Explain why it is not possible to use the information from this table to calculate the exact value of the mean time taken. 

Ceri records the time taken, minutes, to travel to school for a sample of 168 students at her Academy.

Time taken ( minutes)	Frequency
	54
	50
	44
	20

Ceri says

The longest time that any of these students took to travel to school was 80 minutes.

Is she correct?
Give a reason for your answer.

Ceri also claims that 25% of all of the students at this Academy took more than 30 minutes to travel to school.

[2]

[1]

Jenny has six cards.

Each card has a whole number written on it so that

the smallest number is 5
the largest number is 24
the median of the six numbers is 14
the mode of the six numbers is 8

Jenny arranges her cards so that the numbers are in order of size.

For the remaining four cards, write on each dotted line a number that could be on the card.

Diyar recorded the distance, in kilometres, that he cycled each day for 11 days.
Here are his results.

Find the interquartile range of his results.

....................................................... km

Yusuf sat 8 examinations.
Here are his marks for 5 of the examinations.

For his results in all 8 examinations

the mode of his marks is 80
the median of his marks is 74
the range of his marks is 16

Find Yusuf’s marks for each of the other 3 examinations.

Given that 
the four whole numbers and have

a mode of 7
a median of 8.5
a mean of 9

Work out the value of a, the value of b and the value of .

Sandeep sat  tests in January 
Each test was marked out of 

Here are his test results.

Find the interquartile range of these test results.
Show your working clearly.

Sandeep also sat some tests in May 
Each test was marked out of 

The median of the May  test results is 
The interquartile range of the May  test results is 

In which month, January or May, were Sandeep’s test results more consistent?
Give a reason for your answer.

Circle the expression for the range of consecutive integers.

Here is some information about the times taken by 40 people to fill in a form.

Time,  minutes	Number of people
	3
	9
	11
	17

In which class interval is the median?
Circle your answer.

102 boys and 85 girls took a test.

The table shows information about the mean marks.

The pass mark for the test was 70
Was the mean mark for all of these students greater than the pass mark?
You must show your working.

Here is some information about 26 houses.

and are all different numbers.

Number of bedrooms	Number of houses
1	7
2
3
4
5	8

The median number of bedrooms is 3.5

Work out a possible set of values for and .

200 people recorded the time they spent on social media one day.

The table shows the results.

Time, t (mins)	Frequency	Midpoint
	24
	76
	52
	48
	Total = 200

Work out an estimate of the mean time.

..................................mins

The table shows information about the distances walked by 120 students on their way to school one week.

Distance,  (miles)	Frequency
	20
	48
	30
	22
	Total = 120

Work out an estimate for the mean distance.

...................miles