Advanced Math 45S
Statistics Hand In Assignment
Statistics Assignment
Name:
BCI / HCI / MP
1. You have been asked to form a committee of 10 people from your school, that has 20 students
in Grade 9, 25 students in grade 10, 30 students in grade 11 and 15 students in grade 12.
Describe how you could take a sample that was representative of the students in your school.
(Be specific – use numbers!) (4 marks)
2. A total of 3286 students wrote a University entrance exam. Kale and 432 other students had a
score of 891 out of 1200. There were 2279 students who scored lower than 891.
a. What was Kale’s percentile ranking?
(2 marks)
b. To apply for an entrance scholarship Kale had be in the top 30%. Did he score high
enough to apply for the scholarship? Justify your answer.
(2 marks)
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Advanced Math 45S
Statistics Hand In Assignment
3. Bob received the following grades during his Advanced Math class.
82
94
87
97
94
73
85
Calculate the mean, median and mode of this data. (3 marks)
Mean:
Median:
Mode:
Which measure of central tendency should he use to show that he is getting high scores? Justify
your choice. (2 marks)
Which measure of central tendency do YOU think best represents his scores in this class? Justify
your choice. (2 marks)
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Advanced Math 45S
Statistics Hand In Assignment
4. Using the data table below:
x
10-20
20-30
30-40
40-50
50-60
Calculate:
a) The mean (2 marks)
b) The median (2 marks)
c) The modal group (1 mark)
d) The standard deviation (2 marks)
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frequency
5
7
15
3
5
Mid-pt
Advanced Math 45S
Statistics Hand In Assignment
5. The data below show the cost (in cents) of 40 meals at a fast-food outlet. Put the data into
suitable groups and complete the frequency table (3 marks)
Cost (cents)
400
420
425
445
445
445
450
450
455
460
470
470
470
470
475
475
475
475
480
480
480
480
490
490
495
495
510
515
515
515
520
530
530
535
540
565
570
580
580
585
b) Draw a Histogram of the data. (4 marks)
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Tally
Frequency
Advanced Math 45S
Statistics Hand In Assignment
6a) The marks obtained by 80 students in an examination are shown below. Complete the cumulative
frequency table. (1 mark)
Mark
1-10
11-20
21-30
31-40
41-50
51-60
61-70
71-80
81-90
91-100
Frequency
3
5
5
9
11
15
14
8
6
4
Cumulative Frequency
b) Plot a cumulative frequency curve of the data above (4 marks)
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Advanced Math 45S
Statistics Hand In Assignment
b) Using the cumulative frequency graph to estimate the median, Lower and Upper
quartiles and the Inter Quartile Range (4 marks)
Median =
Lower Quartile (Q1) =
Upper Quartile (Q1) =
Interquartile Range (IQR) =
c) Draw a box and whisker plot of the data (4 marks)
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Advanced Math 45S
Statistics Hand In Assignment
7. Given that 120 students take an examination, and assuming that the distribution of marks is
normally distributed with a mean of 72 and a standard deviation of 5, find:
a. Percentage of students who got over 80% (3 marks)
b. Number of students who got less than 65% (4 marks)
c. Number of students who got between 65% and 75% on the test. (4 marks)
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Advanced Math 45S
Statistics Hand In Assignment
d. If the prof wants the top 8% of students to get an A what mark will be the boundary? (3
marks)
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