Browse Averages & range

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Mean, median, mode & range

15 questions

LessonNot started
Seven pupils each solved a puzzle. Their times, in seconds, were:

3241383544393632 \quad 41 \quad 38 \quad 35 \quad 44 \quad 39 \quad 36

(a) Work out the median of these seven times.

(b) Write down the range of these seven times.

An eighth pupil then solves the puzzle in 115115 seconds.

(c) Work out the median of all eight times.

(d) Write down the range of all eight times.

(e) The mean of all eight times is 47.547.5 seconds. Explain why the median is a better description of a typical time for these eight pupils than the mean is.
●●●●●Level 47 marksStart
A small company has nine employees. Their annual salaries are:

£19 000, £21 000, £22 000, £21 000, £24 000, £23 000, £21 000, £26 000, £120 000

(a) Work out the mean salary.

(b) Work out the median salary.

(c) The owner wants to quote a single figure as "a typical salary at this company". State which of the mean and the median is the fairer figure to quote, and give a reason for your answer.

(d) The company also records the department each of the nine employees works in:

Sales, Sales, Admin, Sales, Workshop, Admin, Sales, Workshop, Admin

Write down the modal department, and explain why neither the mean nor the median can be used for this data.
●●●●●Level 48 marksStart
Here are five numbers.

127159x12 \quad 7 \quad 15 \quad 9 \quad x

The mean of the five numbers is 1313.

(a) Work out the value of xx.

(b) Work out the median of the five numbers.
●●●●●Level 45 marksStart
The table gives some information about the lengths, in minutes, of 6060 films shown at a film festival.
Length (minutes)
Shortest length8484
Longest length152152
Lower quartile9797
Upper quartile121121
Median108108
(a) Draw a box plot to represent this information.8090100110120130140150160Length (minutes)(3 marks)
(b) Work out an estimate for the number of these films with a length between 9797 minutes and 121121 minutes.

(1 mark)

Oscar says,

"The median is 108108 minutes, so one of the films must be exactly 108108 minutes long."
(c) Is Oscar correct? Give a reason for your answer.

(1 mark)
●●●●●Level 45 marksStart

Averages from a frequency table

12 questions

LessonNot started
The table gives information about the number of days each of 60 students was absent last term.
Number of days absent, xxFrequency, ff
018
115
212
39
44
52
(a) Write down the range of the number of days absent.

(b) Work out the median number of days absent.

(c) Work out the mean number of days absent. Give your answer correct to 2 decimal places.
●●●●●Level 46 marksStart
A shop recorded the number of items bought by each of 80 customers. One frequency has been left out of the table.
Number of items, xxFrequency, ff
126
221
3
49
56
(a) Work out the missing frequency.

(b) Work out the mean number of items bought per customer.
●●●●●Level 45 marksStart
The table shows the number of pets owned by each of the 24 pupils in a class.
Number of pets, xxFrequency, ff
09
17
25
32
41
(a) Work out the mean number of pets owned by these 24 pupils.

(b) Six more pupils join the class. Each of these six pupils owns 3 pets.

Work out the mean number of pets owned by all 30 pupils.
●●●●●Level 46 marksStart

Estimating averages from grouped data

15 questions

LessonNot started
The table shows information about the amount, £mm, spent by each of 50 customers in a shop.
Amount spent, £mmFrequency
0<m≤100 < m \le 1012
10<m≤2010 < m \le 2020
20<m≤3020 < m \le 3013
30<m≤6030 < m \le 605
(a) Work out an estimate for the mean amount spent by a customer.

(b) The manager checks the till and finds that each of the 5 customers in the last class actually spent less than £40.

Explain what this tells you about your estimate in part (a).
●●●●●Level 45 marksStart
The table shows information about the lengths, cc minutes, of 90 phone calls made from an office.
Length, cc (minutes)Frequency
0<c≤50 < c \le 524
5<c≤105 < c \le 1031
10<c≤1510 < c \le 1520
15<c≤2015 < c \le 2015
(a) Find the class interval that contains the median.

(b) Work out an estimate for the mean length of a call. Give your answer correct to 1 decimal place.

(c) Sam says that the median must be exactly the midpoint of the class interval found in part (a).

Explain why Sam is wrong.
●●●●●Level 47 marksStart