Download Introductory Statistics – 4930AS

Introductory Statistics – 4930AS
Assignment 3
This assignment is part three of five parts that make up the Teacher Item for your
portfolio. The questions are directly related to the assessment criteria for LO3. The
assignment should be neatly hand-written, and submitted to your teacher for marking.
When it is returned, file it in your portfolio.
1.
For what reason would you find the centre of a data set?
2.
Calculate the mean, median and mode for each of the following data sets:
(a) { 30, 55, 64, 74, 51, 10, 82 }
(b) { 44, 31, 66, 2, 75, 96, 15, 96 }
(c) { 1.5, 3.5, 6.3, 0.5, 7.2, 8.5, 3.5, 1.5, 9.9 }
(d) { 0.47, 0.31, 0.12, 0.25, 0.53, 0.16, 0.16, 2.08 }
3.
For each of (a), (b), (c) and (d) in Question 2, say which measure of centre you
think is most suitable.
4.
Calculate the mean, median and mode for each of the following frequency
distributions:
(a)
(b)
x
f
x
f
0
10
1
4
1
17
2
7
2
28
3
3
3
33
4
7
4
25
5
5
5
16
(c)
(d)
x
10
13
15
16
19
20
5.
f
4
1
10
2
8
5
x
0.2
0.4
0.6
0.8
1.0
1.2
f
34
23
18
10
4
1
A class of 18 students has the following ages:
21 24 21 19 25 30 21 23 23
20 24 41 36 32 28 21 19 20
(a) Organise the data into a frequency table.
(b) Find the mean and median age of the students.
6.
The following tables show the distribution of examination scores for two classes
of TPC students:
Class X
Scores
f
2
0  10
16
10  20
28
20 30
11
30  40
1
40  50
Class Y
Scores
f
2
0  10
17
10  20
10
20 30
18
30  40
6
40  50
(a) Draw a cumulative frequency polygon (ogive) for each class, X and Y, and
find an estimate for the median and interquartile range in each case.
(b) Compare the performance of classes X and Y in terms of centre and spread.
7.
The following data represents the weights of 20 people living in Maple Avenue,
recorded to the nearest kilogram:
35
63
52
79
61
50
70
59
41
67
56
91
61
49
75
57
47
66
57
83
(a)
(b)
(c)
(d)
(e)
Draw a stem and leaf diagram.
What is the range of the data?
What is the median weight?
Find Q1 and Q3, and the interquartile range.
Copy and complete this statement: “The middle 50% of weights of the people
living in Maple Avenue lie between
kg and
kg”.
(f) Calculate the mean and standard deviation, correct to two decimal places.
(g) What proportion of the weights in this sample are within one standard
deviation of the mean?
(h) Construct a grouped frequency distribution table, with class intervals 30 40,
40 50 etc. Include a column for the class midpoint.
(i) Using your table in (h), calculate the mean and standard deviation of the
grouped data, correct to two decimal places.
(j) Are your answers to (i) different from those in (f)? Why?
(k) Add a column to your table in (i) for cumulative frequency.
(l) Draw a cumulative frequency histogram and polygon using the grouped data.
(m) Use the cumulative frequency polygon to estimate the median of the grouped
data. Is your estimate the same as the actual median weight found in (c)?
8.
(a) Explain what the standard deviation of a set of scores is, and what it tells you.
(b) Define the variance of a set of scores.
(c) The following marks were obtained by six students in a maths test:
4
7
8
5
5
7
Calculate
(i)the mean, and
(ii)the mean deviation of the scores.
9.
The number of runs scored by Jack and Bill in seven cricket matches were:
Jack:
Bill:
85
38
17
42
24
31
19
45
40
27
9
36
48
25
(a) Find the mean and standard deviation for each set of scores.
(b) Who had the higher average score?
(c) Who was the most consistent batter? Give a reason for your answer.
10. Students from two schools were given a general knowledge test and the results
were analysed to compare the results of the two schools. Test scores between 0
and 60 were possible, and the results are shown in the box-and-whisker plots.
School A
School B
0
10
20
30
Marks
40
50
(a) Write down a five-point summary for each school.
(b) Describe the distribution of scores for each school.
(c) Compare the performance of the two schools on this test.
End of assignment
60