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18.06 Frequency tables

Worksheet
Data and frequency tables
1

Complete the frequency table below based on the following data set:

2,\, 5,\, 4,\, 5,\, 5,\, 5,\, 3,\, 4,\, 5,\, 5,\, 1,\, 3,\, 3,\, 3,\, 5,\, 2,\, 4,\, 1,\, 6,\, 5,\, 6,\, 3,\, 1,\, 1,\, 6

\text{Score}\text{Frequency}
1
2
3
4
5
6
2

Complete the following frequency tables:

a
\text{Score } (x)\text{Frequency } (f)xf
17
24
37
48
58
68
b
\text{Score}\text{Frequency}\text{Cumulative} \\\ \text{frequency}
45
58
67
77
83
97
3

Construct a cumulative frequency table for each of the following data sets:

a

3,\, 6,\, 4,\, 4,\, 7,\, 5,\, 5,\, 6,\, 2,\, 4,\, 6,\, 5,\, 5,\, 2,\, 3,\, 6,\, 5,\, 3,\, 5,\, 2,\, 5,\, 2,\, 5,\, 6,\, 7

b

5,\, 4,\, 7,\, 8,\, 6,\, 4,\, 9,\, 4,\, 4,\, 8,\, 8,\, 5,\, 6,\, 9,\, 4,\, 9,\, 8,\, 6,\, 6,\, 7,\, 4,\, 4,\, 7,\, 4,\, 8

4

State the mode of the following data set:

\text{Score}\text{Frequency}
33
43
54
62
75
88
5

Find the median for the following data set:

\text{Score}\text{Frequency}\text{Cumulative frequency}
233
358
4311
5415
6823
7225
6

Find the mean for the following data set, correct to one decimal place:

\text{Score } (x)\text{Frequency } (f)xf
2714
326
4832
5525
6424
7749
7

A statistician organised a set of data into the following frequency table:

a

Complete the frequency distribution table.

b

Find the mean, correct to two decimal places.

\text{Score }(x)\text{Frequency }(f)xf
514
74
92
1118
136
\text{Total}
8

Consider the data provided in the table:

a

Find the range.

b

Find the mode.

\text{Score}\text{Frequency}
6816
6941
7030
7131
7249
7329
9

Consider the following data set:

27,\, 25,\, 24,\, 24,\, 24,\, 24,\, 24,\, 25,\, 23,\, 24,\, 26,\, 23,\, 27,\\ 23,\, 24,\, 27,\, 23,\, 23,\, 27,\, 25,\, 24,\, 24,\, 27,\, 25,\, 23

a

Construct a frequency distribution table for the data.

b

Find the mean, correct to one decimal place.

c

Find the range.

d

Find the mode.

Grouped data and frequency tables
10

Complete the frequency table below based on the following data set:

36,\, 50,\, 66,\, 46,\, 78,\, 63,\, 58,\, 39,\, 84,\, 40,\, 81,\, 45,\, 86,\\ 51,\, 68,\, 43,\, 64,\, 67,\, 37,\, 68,\, 48,\, 65,\, 60,\, 82,\, 75

\text{Class}\text{Frequency}
30 - 39
40 - 49
50 - 59
60 - 69
70 - 79
80 - 89
11

Complete the frequency table below based on the following data set:

25,\, 49,\, 27,\, 34,\, 28,\, 46,\, 21,\, 47,\, 36,\, 43,\, 41,\, 37,\, 37,\\ 23,\, 36,\, 37,\, 43,\, 48,\, 36,\, 40,\, 34,\, 39,\, 29,\, 46,\, 30

\text{Class}\text{Class centre } (x)\text{Frequency } (f)xf
21 - 2523
26 - 3028
31 - 3533
36 - 4038
41 - 4543
46 - 5048
12

Complete the following frequency tables:

a
\text{Class}\text{Frequency}\text{Cumulative frequency}
10 - 193
20 - 299
30 - 399
40 - 494
50 - 592
60 - 697
b
\text{Class}\text{Class centre } (x)\text{Frequency } (f)xf
11 - 15136
16 - 20188
21 - 25232
26 - 30282
31 - 35335
36 - 40381
13

Construct a cumulative frequency table for the following data set. Use class intervals of 40 - 49, 50 - 59, 60 - 69, etc.

77,\, 54,\, 53,\, 56,\, 73,\, 55,\, 94,\, 95,\, 76,\, 52,\, 72,\, 46,\, 85,\\ 61,\, 48,\, 90,\, 64,\, 70,\, 40,\, 52,\, 57,\, 88,\, 59,\, 95,\, 61

14

Consider the following frequency table:

a

Complete the table.

b

Calculate an estimate for the mean. Round your answer to two decimal places.

\text{Class}\text{Class} \\ \text{centre } (x)fxf
1 - 98
10 - 186
19 - 274
28 - 366
37 - 458
\text{Total}
15

State the modal class of the following data set:

\text{Class}\text{Frequency}
30 - 398
40 - 495
50 - 594
60 - 693
70 - 793
80 - 892
16

Estimate the median for the following data set:

\text{Class}\text{Frequency}\text{Cumulative frequency}
21 - 2544
26 - 3037
31 - 35310
36 - 40212
41 - 45517
46 - 50825
17

Estimate the mean for the following data set, correct to one decimal place:

\text{Class}\text{Class centre } (x)\text{Frequency } (f)xf
6 - 108216
11 - 1513113
16 - 20189162
21 - 25238184
26 - 30287196
31 - 35335165
18

Consider the frequency table:

a

Estimate the mean, correct to one decimal place.

b

State the modal group of scores.

\text{Score}\text{Frequency}
1 - 520
6-1015
11 - 158
16 - 204
21 - 253
26 - 302
Applications
19

Mr. Rodriguez recorded the number of pets owned by each of the students in his class. He found that 14 people had no pets, 17 people had one pet, 5 people had two pets and 9 people had three pets.

a

Construct a frequency table of the data.

b

How many students were surveyed?

c
How many pets were owned in total?
d
Calculate the mean number of pets owned by Mr Rodriguez's students.
20

The frequency table below shows the resting heart rate of some people taking part in a study:

a

Complete the frequency table.

b

Use the class centres to estimate the mean resting heart rate, to two decimal places.

\text{Heart rate}\text{Class}\\ \text{centre } (x)\text{Freq.}(f)xf
30-3913
40-4922
50-5924
60-6936
21

Ben asked 35 people about how many siblings they have. He found that 12 people had no siblings, 15 people had one sibling, 3 people had two siblings and 5 people had three siblings.

a

Construct a frequency table of Ben's results.

b
Find the mode of the data.
c
Find the range of the data.
22

In a survey the mass (in grams) of 30 individual apples from an orchard were noted and recorded in the following list:

86,\quad 87,\quad 91,\quad 93,\quad 94,\quad 95,\quad 96,\quad 96,\quad 98,\quad99

100,\quad 101,\quad 102,\quad 103,\quad 103,\quad 104,\quad 104,\quad 105,\quad 106,\quad 106

106,\quad 107,\quad 107,\quad 107,\quad 108,\quad 108,\quad 109,\quad 109,\quad 109,\quad 109

a

Complete the given frequency table.

b

Using the class centres, estimate the median.

c

How does this compare to the median in the individual data? Explain your answer.

\text{Weight (g)}\text{Class} \\ \text{centre}\text{Frequency}
85\leq x \lt 9087.5
90\leq x \lt 953
95\leq x \lt 100
100\leq x \lt 105
105\leq x \lt 110
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Outcomes

MA4-19SP

collects, represents and interprets single sets of data, using appropriate statistical displays

MA4-20SP

analyses single sets of data using measures of location, and range

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