Assessed Homework FM-3d
1.
a)
Statistics Book 1 Ch1-4
Give an advantage and a disadvantage of stratified sampling
(2)
b) A school contains, 120 Year 12 boys, 65 Year 12 girls, 105 Year 13 boys and 75 Year 13 girls.
If a stratified sample of 30 is needed, how many from each group should be included in the sample?
(5)
7 marks
2.
Describe the following data types:
3 marks
3.
The following marks out of 50 were obtained in an exam:
a)
Hair colour
b) Hair length
2, 23, 25, 27, 29, 29, 30, 31, 33, 35, 35, 38, 40, 42, 45, 46, 49
a)
b)
c)
4.
5.
6.
Find the median and the quartiles.
Identify any outliers using a definition of 1.5×IQR
Find the standard deviation
(You must show your working for all parts of this question.)
(4)
(4)
(3)
11 marks
A set of 25 measurements was taken, and the mean found to be 18, and the standard deviation 3.
However, one measurement was incorrectly recorded as 30 when it should have been 13.
What is the true mean and standard deviation of the measurements?
8 marks
A set of 𝑚 numbers has mean 𝑘, and another set of 𝑛 numbers has mean 𝑝.
If all the numbers in the first set are tripled and then combined with the second set (not tripled),
what will the mean be of the combined set of numbers? (Show your working.)
5 marks
The data shows heights of trees (in metres) in an orchard.
Height h / m
2.5 ≤ h < 3.0
3.0 ≤ h < 3.8
3.8 ≤ h < 4.4
4.4 ≤ h < 5.4
5.4 ≤ h < 7.0
Frequency
4
10
12
9
5
a) Calculate estimates for the median and the 15% to 85% inter-percentile range
b) Calculate an estimate for the standard deviation
c) If the data were put into a histogram, calculate the heights (with k=1, i.e. frequency densities) of the
first two bars
7.
(5)
(4)
(2)
11 marks
The time taken by an office worker to set up, type, and save 8 different documents is shown below:
Words
250
420
196
334
367
578
518
476
Time (seconds)
318
515
250
431
436
602
591
582
The equation of the regression line of t (time) on w (words) is 𝑡 = 0.979𝑤 + 81.6
a) Use the regression line to estimate the time needed to set up, type and save a document of 530 words
b) Give an interpretation of the value 81.6 in the regression equation
c) Would it be appropriate to use this equation to calculate the time needed to set up, type and save a
document of 25,000 words? Give a reason for your answer.
(2)
(1)
(2)
5 marks
TOTAL: 50 MARKS
Page 1 of 1
KEGS Mathematics © 2019
A-Level Mathematics – Cornerstone Skills for Building Resilient Problem Solvers
1. Algebraic & numeric fluency
2. Calculator skill & IT literacy
3. Graphs & Constructions
4. Comprehension & Interpretation