Descriptive Statistics Study Guide
1. State whether these data are discrete or
continuous.
A)
The heights of bonsai trees
B)
The shoe sizes of the All Star rugby team
C)
The numbers of differently colored hats on
a market stall
D)
The weights of baby chimpanzees
E) The time taken for students to write their
extended essays
F) The marks obtained by grade 9 in a French test
G)
The weights of ten pieces of sushi
H)
The hours of sunlight each day during the
month of July
I) The scores obtained when a dart is thrown 50
times
J) The times taken for students in grade 11 to walk
500 m
K)
The number of visitors to Niagara Falls each
day
L) The exact weights of 100 one-kg bags of rice
2. Sixty people were asked how often they
traveled by metro (underground railway) each
month. The results are shown below.
26
20
10
30
80
38
62
36
46
40
14
22
4
10
20
42
6
8
76
38
30
48
68
24
38
68
12
32
50
10
4
20
10
8
48
22
60
44
16
32
42
8
28
22
6
76
16
14
44
64
56
34
46
20
8
16
74
12
16
6
A) Represent this information in a grouped
frequency table
B) Draw a histogram to represent the
information graphically.
3. The number of hours of CAS completed in the first
term for the 80 students at Idowell School is recorded
below.
16
32
8
41
27
103
19
31
42
6
21
51
13
38
72
80
20
61
82
73
10
36
25
39
65
101
10
49
43
78
33
25
27
26
83
94
14
53
51
85
45
41
92
18
29
63
81
102
32
29
9
18
15
32
41
52
33
100
28
48
19
98
39
19
40
73
61
97
19
73
63
64
41
27
70
28
55
88
46
95
Represent this information in an ordered stem and leaf
diagram.
4. The table shows the number of piglets in a litter.
Number of piglets
6
7
8
9
10
11
12
13
14
Frequency
8
15
16
20
22
7
4
2
1
a) Find the lower quartile, the median and the upper
quartile
b) Draw a box and whisker plot to represent the
information
c) Are there any outliers?
5. Hans studied an article in Die Welt. He recorded
the number of words in each sentence as shown in
the frequency table.
Number of Words
Frequency
1–5
6
6 – 10
28
11 – 15
36
16 – 20
14
21 – 25
10
26 – 30
3
31 – 35
1
36 – 40
0
41 - 45
2
a) Draw a cumulative frequency graph to represent
this information.
b) Write down the lower quartile, the median, and
the upper quartile.
c) Given that the smallest sentence had one word
and the largest had 43 words, draw a box and
whiskers plot.
6. The reaction times of 50 children for catching a
ruler are shown in the table.
Time (s)
Frequency
0≤s<1
3
1≤s<2
10
2≤s<3
14
3≤s<4
15
4≤s<5
4
5≤s<6
2
6≤s<7
1
7≤s<8
1
a) Write down the modal class
b) Find an approximation for the median and mean
times.
7. The mean weight of ten
pineapples is 0.526 kg. Two
more pineapples weighing
0.638 kg and 0.589 kg
respectively are added to the
other ten. Calculate the mean
weight of all twelve pineapples.
8. The times taken for 30 camels to cover a
distance of 10 km are given in the table.
Time Taken (min)
50 ≤ s < 55
55 ≤ s < 60
60 ≤ s < 65
65 ≤ s < 70
70 ≤ s < 75
75 ≤ s < 80
80 ≤ s < 85
Frequency
2
8
10
3
4
2
1
a) Draw a cumulative frequency graph to
find the interquartile range of the time
taken
b) Calculate an approximate value for the
standard deviation of the times taken.
9. Calculate the mean
and standard deviation
for these data.
6 3 8 5 2 9
11 21 15 8
10. The mean of ten
numbers is 5.5
4 3 a 8 7 3 9
5 8 3
A) Find the value of a
B) Find the median of
these numbers