### Statistics Worksheet 4: Class Discussion (Suggested Responses)

Question 1

(a) Mean = 56.0 cm

(b) The tailor would not choose the mean because, the mean may or may not be one of the head sizes. It may land up not fitting into any students' head at all.
(c) The moal head measurement is 55.5 cm
(d) Yes, it does since it means it has the highest number of students having this head measurement.
(e) The mode.
Question 2
(a) Mean salary
= [(\$850 x 2) + (\$700 x 2) + (\$650 x 4) + (\$600 x 1)] ÷ 9
= \$6300 ÷ 9
= \$700
(b) As the salary amongst the employees are quite close to each other, therefore the mean is a good 'representative' of data on salaries of this firm.
(c) \$700
Question 3
(a) The mean salary becomes \$830
(b) The mean salary is no longer a good representative of the earnings of the employees.
(c) By arranging the salaries in ascending order:
\$600, \$650, \$650, \$650, \$650, \$700, \$700, \$850, \$850, \$2000
The median salary now occurs between the 5th and 6th positions, which is the average of the \$650 and \$700.
Median = \$675
(d) Yes, the median gives a better indication of the average salary of the employees.
(e) Mode = \$650
(f) Mode is chosen as it is the pay that "most" people are paid.
Question 4
The median of the numbers 1, 2, 4, y, 7 and 8 is 5.
Find the value of y.
Since there are 6 numbers, hence the median would be between the 3rd & 4th numbers.
3rd number is 4
4th number is y
Since the median is average of 4 and y, therefore (4+y)/2 = 5
i.e. 4 + y = 10
and therefore y = 6
Question 5
The median of the numbers 13, 17, 16, 11, 12, 15 and z is z. Find the possible values of z.
Arranging 6 numbers in ascending order (without z)
11, 12, 13, 15, 16, 17
If z is the median, it will be in the 4th position.
Hence, arranging the 7 numbers in ascending order:
11, 12, 13, z, 15, 16, 17
Since z is the median, it could take any value from 13 to 15.
In other words, if z is a whole number, then it could be 13, 14 or 15.
However, if z is a real number, it would be 13 ≤ z ≤ 15
You may ask questions (via Comments) if you think there are other ways to interpret and answer to the questions.