chapter 85 presentation of statistical data AWS
CHAPTER 85 PRESENTATION OF STATISTICAL DATA EXERCISE 323 Page 906
1. State whether data relating to the topics given are discrete or continuous: (a) The amount of petrol produced daily, for each of 31 days, by a refinery. (b) The amount of coal produced daily by each of 15 miners. (c) The number of bottles of milk delivered daily by each of 20 milkmen. (d) The size of 10 samples of rivets produced by a machine.
(a) Continuous – could be any amount of petrol (b) Continuous – could be any amount of coal (c) Discrete – can only be a whole number of bottles of milk (d) Continuous – could be any size of rivet
2. State whether data relating to the topics given are discrete or continuous: (a) The number of people visiting an exhibition on each of 5 days. (b) The time taken by each of 12 athletes to run 100 metres. (c) The value of stamps sold in a day by each of 20 post offices. (d) The number of defective items produced in each of 10 one-hour periods by a machine.
(a) Discrete – can only be a whole number of people (b) Continuous – could be any time taken (c) Discrete – can only be a whole number of stamps (d) Discrete – can only be a whole number of defective items
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EXERCISE 324 Page 909
1. The number of vehicles passing a stationary observer on a road in 6 ten-minute intervals is as shown. Draw a pictogram to represent these data. Period of time
1 2
3 4
5 6
Number of vehicles 35 44 62 68 49 41 If one symbol is used to represent 10 vehicles, working correct to the nearest 5 vehicles gives 3.5, 4.5, 6, 7, 5 and 4 symbols, respectively, as shown below.
2. The number of components produced by a factory in a week is as shown below: Day
Mon
Tues
Wed
Thur
Fri
Number of components
1580
2190
1840 2385 1280
Show these data on a pictogram.
If one symbol represents 200 components, working correct to the nearest 100 components gives: Mon 8, Tues 11, Wed 9, Thurs 12 and Fri 6.5
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3. For the data given in Problem 1, draw a horizontal bar chart.
A horizontal bar chart is shown below
4. Present the data given in Problem 2 on a horizontal bar chart.
A horizontal bar chart is shown below
5. For the data given in Problem 1, construct a vertical bar chart.
A vertical bar chart is shown below
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© 2014, John Bird
6. Depict the data given in Problem 2 on a vertical bar chart.
A vertical bar chart is shown below
7. A factory produces three different types of components. The percentages of each of these components produced for 3 one-month periods are as shown below. Show this information on percentage component bar charts and comment on the changing trend in the percentages of the types of component produced. Month
1
2
3
Component P
20
35
40
Component Q
45
40
35
Component R
35
25
25 1336
© 2014, John Bird
The information is shown on the percentage component bar chart below It is seen that P increases by 20% at the expense of Q and R
8. A company has five distribution centres and the mass of goods in tonnes sent to each centre during 4 one-week periods is as shown. Week
1
2
3
4
Centre A
147
160
174
158
Centre B
54
Centre C
63
77
69
283
251 237
211
Centre D
97
104 117
144
Centre E
224
218
194
203
Use a percentage component bar chart to present these data and comment on any trends.
Week 1: Total = 147 + 54 + 283 + 97 + 224 = 805 A=
147 54 ×100% ≈ 18% , B = ×100% ≈ 7% , C ≈ 35%, D ≈ 12%, E ≈ 28% 805 805
Week 2: Total = 160 + 63 + 251 + 104 + 218 = 796 A=
160 63 ×100% ≈ 20% , B = ×100% ≈ 8% , C ≈ 32%, D ≈ 13%, E ≈ 27% 796 796
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Week 3: Total = 174 + 77 + 237 + 117 + 203 = 808 A=
174 77 ×100% ≈ 10% , C ≈ 29%, D ≈ 14%, E ≈ 25% ×100% ≈ 22% , B = 808 808
Week 4: Total = 158 + 69 + 211 + 144 + 194 = 776 A=
158 69 ×100% ≈ 20% , B = ×100% ≈ 9% , C ≈ 27%, D ≈ 19%, E ≈ 25% 776 776
A percentage component bar chart is shown below
From the above percentage component bar chart, it is seen that there is little change in centres A and B, there is a reduction of around 8% in centre C, an increase of around 7% in centre D and a reduction of about 3% in centre E
9. The employees in a company can be split into the following categories: managerial 3, supervisory 9, craftsmen 21, semi-skilled 67, others 44 Show these data on a pie diagram.
Number of employees = 3 + 9 + 21 + 67 + 44 = 144 1 employee corresponds to 360 ×
1 =2.5° 144
Hence, 3 employees corresponds to 3 × 2.5 = 7.5°, 9 employees corresponds to 9 × 2.5 = 22.5° Similarly, 21, 67 and 44 employees correspond to 52.5°, 167.5° and 110°, respectively
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© 2014, John Bird
A pie diagram is therefore a circle of any radius, subdivided into sectors having angles of 7.5°, 22.5°, 52.5°, 167.5° and 110°, respectively, as shown below
10. The way in which an apprentice spent his time over a one-month period is as follows: drawing office 44 hours, production 64 hours, training 12 hours, at college 28 hours Use a pie diagram to depict this information.
Total hours = 44 + 64 + 12 + 28 = 148 Drawing office, D = Training, T =
44 × 360° ≈ 107° , 148
12 × 360° ≈ 29° , 148
Production, P = College, C =
64 × 360° ≈ 156° , 148
28 × 360° ≈ 68° 148
A pie chart to depict this information is shown below.
11. (a) With reference to Figure 85.5, determine the amount spent on labour and materials to produce 1650 units of the product. (b) If in year 2 of Figure 85.4, 1% corresponds to 2.5 dwellings, how many bungalows are sold in that year
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© 2014, John Bird
(a) Each product costs £2. Hence, 1650 units will cost £2 × 1650 = £3300 (Labour + materials) represents (36° + 18° = 44°) of 360°, i.e.
Hence, labour and material costs =
54 of total 360
54 54 of £3300 = × £3300 = £495 360 360
(b) In year 2 bungalows account for 7 + 28 = 35% of annual sales If 1% corresponds to 2.5 dwellings, then number of bungalows sold = 35 × 2.5 = 87.5 = 88 correct to nearest whole number
12. (a) If the company sell 23 500 units per annum of the product depicted in Figure 85.5, determine the cost of their overheads per annum. (b) If 1% of the dwellings represented in year 1 of Figure 85.4 corresponds to two dwellings, find the total number of houses sold in that year.
(a) Overheads =
126 ×100% = 35% of total costs 360
Cost per unit = £2, hence total income per annum = 23 500 × 2 = £47 000 Cost of overheads per annum = 35% of £47 000 =
35 × 47 000 = £16 450 100
(b) Percentage of houses sold in year 1 = 22 + 32 + 15 = 69% If 1% corresponds to two dwellings then the number of houses sold = 69 × 2 = 138 houses
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EXERCISE 325 Page 915
1. The mass in kilograms, correct to the nearest one-tenth of a kilogram, of 60 bars of metal are as shown. Form a frequency distribution of about eight classes for these data. 39.8 40.1 40.3 40.0 40.6 39.7 40.0 40.4 39.6 39.3 39.6 40.7 40.2 39.9 40.3 40.2 40.4 39.9 39.8 40.0 40.2 40.1 40.3 39.7 39.9 40.5 39.9 40.5 40.0 39.9 40.1 40.8 40.0 40.0 40.1 40.2 40.1 40.0 40.2 39.9 39.7 39.8 40.4 39.7 39.9 39.5 40.1 40.1 39.9 40.2 39.5 40.6 40.0 40.1 39.8 39.7 39.5 40.2 39.9 40.3 The range of values is 39.3–40.8. With eight classes therefore the classes chosen are 39.3–39.4, 39.5–39 6, and so on. A tally diagram is shown below with eight classes
A frequency distribution is shown below Class
Class mid-point
Frequency
39.3–39.4
39.35
1
39.5–39.6
39.55
5
39.7–39.8
39.75
9
39.9–40.0
35.95
17
40.1–40.2
40.15
15
40.3–40.4
40.35
7
40.5–40.6
40.55
4
40.7–40.8
40.75
2
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2. Draw a histogram for the frequency distribution given in the solution of Problem 1.
A histogram for the frequency distribution given in the solution of Problem 1 is shown below
3. The information given below refers to the value of resistance in ohms of a batch of 48 resistors of similar value. Form a frequency distribution for the data, having about six classes, and draw a frequency polygon and histogram to represent these data diagramatically. 21.0 22.4 22.8 21.5 22.6 21.1 21.6 22.3 22.9 20.5 21.8 22.2 21.0 21.7 22.5 20.7 23.2 22.9 21.7 21.4 22.1 22.2 22.3 21.3 22.1 21.8 22.0 22.7 21.7 21.9 21.1 22.6 21.4 22.4 22.3 20.9 22.8 21.2 22.7 21.6 22.2 21.6 21.3 22.1 21.5 22.0 23.4 21.2
The range is from 20.5 to 23.4, i.e. range = 23.4–20.5 = 2.9 2.9 ÷ 6 ≈ 0.5 hence, classes of 20.5–20.9, 21.0–21.4, and so on are chosen, as shown in the frequency distribution below 1342
© 2014, John Bird
A frequency polygon is shown below where class mid-point values are plotted against frequency values. Class mid-points occur at 20.7, 21.2, 21.7, and so on.
The histogram for the above frequency distribution is shown below
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© 2014, John Bird
4. The time taken in hours to the failure of 50 specimens of a metal subjected to fatigue failure tests are as shown. Form a frequency distribution having about seven classes and unequal class intervals for these data. 28
22
23 20 12 24 37 28 21 25
21
14
30 23 27 13 23
24
22
26
20
25
23 26 47 21 29 26 22 33
27
9
13 35 20 16 20 25 18 22
7 26 19
3 21 24 28 40 27 24
There is no unique solution, but one solution is: The range of values is 3–47. The seven classes chosen are shown in the tally diagram below
A frequency distribution is shown below Class
Frequency
Lower class boundary 0.5
Class range
3
Upper class boundary 10.5
1–10 11–19
7
19.5
10.5
9
20–22
12
22.5
19.5
3
23–25
11
25.5
22.5
3
26–28
10
28.5
25.5
3
29–38
5
38.5
28.5
10
39–48
2
48.5
38.5
10
1344
10
Height of rectangle
3 = 0.3 10 7 = 0.78 9 12 =4 3 11 = 3.67 3 10 = 3.33 3 5 = 0.5 10 2 = 0.2 10
© 2014, John Bird
5. Form a cumulative frequency distribution and hence draw the ogive for the frequency distribution given in the solution to Problem 3.
A cumulative frequency distribution is shown below Class
Frequency
Upper class boundary Less than
Cumulative frequency
20.5–20.9
3
20.95
3
21.0–21.4
10
21.45
13
21.5–21.9
11
21.95
24
22.0–22.4
13
22.45
37
22.5–22.9
9
22.95
46
23.0–23.4
2
23.45
48
An ogive for the above frequency distribution is shown below
6. Draw a histogram for the frequency distribution given in the solution to Problem 4.
From the frequency distribution in Problem 4, the histogram is shown below
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© 2014, John Bird
7. The frequency distribution for a batch of 50 capacitors of similar value, measured in microfarads, is: 10.5–10.9
2,
11.0–11.4
7,
11.5–11.9
10,
12.0–12.4 12,
12.5–12.9
11,
13.0–13.4
8
Form a cumulative frequency distribution for these data.
A cumulative frequency distribution for the data is shown in the table below Class
Frequency
10.5–10.9
2
Upper class boundary less than 10.95
Cumulative frequency
11.0–11.4
7
11.45
9
11.5–11.9
10
11.95
19
12.0–12.4
12
12.45
31
12.5–12.9
11
12.95
42
13.0–13.4
8
13.45
50
2
8. Draw an ogive for the data given in the solution of Problem 7.
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© 2014, John Bird
An ogive, i.e. a graph of cumulative frequency against upper class boundary values, having coordinates given in the above answer to Problem 7, is shown below
9. The diameter in millimetres of a reel of wire is measured in 48 places and the results are as shown. 2.10
2.29
2.32
2.21
2.14
2.22
2.28
2.18
2.17
2.20
2.23
2.13
2.26
2.10
2.21
2.17
2.28
2.15
2.16
2.25
2.23
2.11
2.27
2.34
2.24
2.05
2.29
2.18
2.24
2.16
2.15
2.22
2.14
2.27
2.09
2.21
2.11
2.17
2.22
2.19
2.12
2.20
2.23
2.07
2.13
2.26
2.16
2.12
(a) Form a frequency distribution of diameters having about 6 classes. (b) Draw a histogram depicting the data. (c) Form a cumulative frequency distribution. (d) Draw an ogive for the data.
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© 2014, John Bird
(a) Range = 2.34–2.05 = 0.29 0.29 ÷ 6 ≈ 0.5, hence classes of 2.05–2.09, 2.10–2.14 and so on are chosen, as shown in the frequency distribution below
(b) A histogram depicting the data is shown below
(c) A cumulative frequency distribution is shown below
Class
Frequency
Upper class boundary Less than
Cumulative frequency
2.05–2.09
3
2.095
3
2.10–2.14
10
2.145
13
2.15–2.19
11
2.195
24
2.20–2.24
13
2.245
37
2.25–2.29
9
2.295
46
2.30–2.34
2
2.345
48
(d) An ogive for the above data is shown below 1348
© 2014, John Bird
1349
© 2014, John Bird
1. State whether data relating to the topics given are discrete or continuous: (a) The amount of petrol produced daily, for each of 31 days, by a refinery. (b) The amount of coal produced daily by each of 15 miners. (c) The number of bottles of milk delivered daily by each of 20 milkmen. (d) The size of 10 samples of rivets produced by a machine.
(a) Continuous – could be any amount of petrol (b) Continuous – could be any amount of coal (c) Discrete – can only be a whole number of bottles of milk (d) Continuous – could be any size of rivet
2. State whether data relating to the topics given are discrete or continuous: (a) The number of people visiting an exhibition on each of 5 days. (b) The time taken by each of 12 athletes to run 100 metres. (c) The value of stamps sold in a day by each of 20 post offices. (d) The number of defective items produced in each of 10 one-hour periods by a machine.
(a) Discrete – can only be a whole number of people (b) Continuous – could be any time taken (c) Discrete – can only be a whole number of stamps (d) Discrete – can only be a whole number of defective items
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© 2014, John Bird
EXERCISE 324 Page 909
1. The number of vehicles passing a stationary observer on a road in 6 ten-minute intervals is as shown. Draw a pictogram to represent these data. Period of time
1 2
3 4
5 6
Number of vehicles 35 44 62 68 49 41 If one symbol is used to represent 10 vehicles, working correct to the nearest 5 vehicles gives 3.5, 4.5, 6, 7, 5 and 4 symbols, respectively, as shown below.
2. The number of components produced by a factory in a week is as shown below: Day
Mon
Tues
Wed
Thur
Fri
Number of components
1580
2190
1840 2385 1280
Show these data on a pictogram.
If one symbol represents 200 components, working correct to the nearest 100 components gives: Mon 8, Tues 11, Wed 9, Thurs 12 and Fri 6.5
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© 2014, John Bird
3. For the data given in Problem 1, draw a horizontal bar chart.
A horizontal bar chart is shown below
4. Present the data given in Problem 2 on a horizontal bar chart.
A horizontal bar chart is shown below
5. For the data given in Problem 1, construct a vertical bar chart.
A vertical bar chart is shown below
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© 2014, John Bird
6. Depict the data given in Problem 2 on a vertical bar chart.
A vertical bar chart is shown below
7. A factory produces three different types of components. The percentages of each of these components produced for 3 one-month periods are as shown below. Show this information on percentage component bar charts and comment on the changing trend in the percentages of the types of component produced. Month
1
2
3
Component P
20
35
40
Component Q
45
40
35
Component R
35
25
25 1336
© 2014, John Bird
The information is shown on the percentage component bar chart below It is seen that P increases by 20% at the expense of Q and R
8. A company has five distribution centres and the mass of goods in tonnes sent to each centre during 4 one-week periods is as shown. Week
1
2
3
4
Centre A
147
160
174
158
Centre B
54
Centre C
63
77
69
283
251 237
211
Centre D
97
104 117
144
Centre E
224
218
194
203
Use a percentage component bar chart to present these data and comment on any trends.
Week 1: Total = 147 + 54 + 283 + 97 + 224 = 805 A=
147 54 ×100% ≈ 18% , B = ×100% ≈ 7% , C ≈ 35%, D ≈ 12%, E ≈ 28% 805 805
Week 2: Total = 160 + 63 + 251 + 104 + 218 = 796 A=
160 63 ×100% ≈ 20% , B = ×100% ≈ 8% , C ≈ 32%, D ≈ 13%, E ≈ 27% 796 796
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© 2014, John Bird
Week 3: Total = 174 + 77 + 237 + 117 + 203 = 808 A=
174 77 ×100% ≈ 10% , C ≈ 29%, D ≈ 14%, E ≈ 25% ×100% ≈ 22% , B = 808 808
Week 4: Total = 158 + 69 + 211 + 144 + 194 = 776 A=
158 69 ×100% ≈ 20% , B = ×100% ≈ 9% , C ≈ 27%, D ≈ 19%, E ≈ 25% 776 776
A percentage component bar chart is shown below
From the above percentage component bar chart, it is seen that there is little change in centres A and B, there is a reduction of around 8% in centre C, an increase of around 7% in centre D and a reduction of about 3% in centre E
9. The employees in a company can be split into the following categories: managerial 3, supervisory 9, craftsmen 21, semi-skilled 67, others 44 Show these data on a pie diagram.
Number of employees = 3 + 9 + 21 + 67 + 44 = 144 1 employee corresponds to 360 ×
1 =2.5° 144
Hence, 3 employees corresponds to 3 × 2.5 = 7.5°, 9 employees corresponds to 9 × 2.5 = 22.5° Similarly, 21, 67 and 44 employees correspond to 52.5°, 167.5° and 110°, respectively
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© 2014, John Bird
A pie diagram is therefore a circle of any radius, subdivided into sectors having angles of 7.5°, 22.5°, 52.5°, 167.5° and 110°, respectively, as shown below
10. The way in which an apprentice spent his time over a one-month period is as follows: drawing office 44 hours, production 64 hours, training 12 hours, at college 28 hours Use a pie diagram to depict this information.
Total hours = 44 + 64 + 12 + 28 = 148 Drawing office, D = Training, T =
44 × 360° ≈ 107° , 148
12 × 360° ≈ 29° , 148
Production, P = College, C =
64 × 360° ≈ 156° , 148
28 × 360° ≈ 68° 148
A pie chart to depict this information is shown below.
11. (a) With reference to Figure 85.5, determine the amount spent on labour and materials to produce 1650 units of the product. (b) If in year 2 of Figure 85.4, 1% corresponds to 2.5 dwellings, how many bungalows are sold in that year
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© 2014, John Bird
(a) Each product costs £2. Hence, 1650 units will cost £2 × 1650 = £3300 (Labour + materials) represents (36° + 18° = 44°) of 360°, i.e.
Hence, labour and material costs =
54 of total 360
54 54 of £3300 = × £3300 = £495 360 360
(b) In year 2 bungalows account for 7 + 28 = 35% of annual sales If 1% corresponds to 2.5 dwellings, then number of bungalows sold = 35 × 2.5 = 87.5 = 88 correct to nearest whole number
12. (a) If the company sell 23 500 units per annum of the product depicted in Figure 85.5, determine the cost of their overheads per annum. (b) If 1% of the dwellings represented in year 1 of Figure 85.4 corresponds to two dwellings, find the total number of houses sold in that year.
(a) Overheads =
126 ×100% = 35% of total costs 360
Cost per unit = £2, hence total income per annum = 23 500 × 2 = £47 000 Cost of overheads per annum = 35% of £47 000 =
35 × 47 000 = £16 450 100
(b) Percentage of houses sold in year 1 = 22 + 32 + 15 = 69% If 1% corresponds to two dwellings then the number of houses sold = 69 × 2 = 138 houses
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© 2014, John Bird
EXERCISE 325 Page 915
1. The mass in kilograms, correct to the nearest one-tenth of a kilogram, of 60 bars of metal are as shown. Form a frequency distribution of about eight classes for these data. 39.8 40.1 40.3 40.0 40.6 39.7 40.0 40.4 39.6 39.3 39.6 40.7 40.2 39.9 40.3 40.2 40.4 39.9 39.8 40.0 40.2 40.1 40.3 39.7 39.9 40.5 39.9 40.5 40.0 39.9 40.1 40.8 40.0 40.0 40.1 40.2 40.1 40.0 40.2 39.9 39.7 39.8 40.4 39.7 39.9 39.5 40.1 40.1 39.9 40.2 39.5 40.6 40.0 40.1 39.8 39.7 39.5 40.2 39.9 40.3 The range of values is 39.3–40.8. With eight classes therefore the classes chosen are 39.3–39.4, 39.5–39 6, and so on. A tally diagram is shown below with eight classes
A frequency distribution is shown below Class
Class mid-point
Frequency
39.3–39.4
39.35
1
39.5–39.6
39.55
5
39.7–39.8
39.75
9
39.9–40.0
35.95
17
40.1–40.2
40.15
15
40.3–40.4
40.35
7
40.5–40.6
40.55
4
40.7–40.8
40.75
2
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© 2014, John Bird
2. Draw a histogram for the frequency distribution given in the solution of Problem 1.
A histogram for the frequency distribution given in the solution of Problem 1 is shown below
3. The information given below refers to the value of resistance in ohms of a batch of 48 resistors of similar value. Form a frequency distribution for the data, having about six classes, and draw a frequency polygon and histogram to represent these data diagramatically. 21.0 22.4 22.8 21.5 22.6 21.1 21.6 22.3 22.9 20.5 21.8 22.2 21.0 21.7 22.5 20.7 23.2 22.9 21.7 21.4 22.1 22.2 22.3 21.3 22.1 21.8 22.0 22.7 21.7 21.9 21.1 22.6 21.4 22.4 22.3 20.9 22.8 21.2 22.7 21.6 22.2 21.6 21.3 22.1 21.5 22.0 23.4 21.2
The range is from 20.5 to 23.4, i.e. range = 23.4–20.5 = 2.9 2.9 ÷ 6 ≈ 0.5 hence, classes of 20.5–20.9, 21.0–21.4, and so on are chosen, as shown in the frequency distribution below 1342
© 2014, John Bird
A frequency polygon is shown below where class mid-point values are plotted against frequency values. Class mid-points occur at 20.7, 21.2, 21.7, and so on.
The histogram for the above frequency distribution is shown below
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© 2014, John Bird
4. The time taken in hours to the failure of 50 specimens of a metal subjected to fatigue failure tests are as shown. Form a frequency distribution having about seven classes and unequal class intervals for these data. 28
22
23 20 12 24 37 28 21 25
21
14
30 23 27 13 23
24
22
26
20
25
23 26 47 21 29 26 22 33
27
9
13 35 20 16 20 25 18 22
7 26 19
3 21 24 28 40 27 24
There is no unique solution, but one solution is: The range of values is 3–47. The seven classes chosen are shown in the tally diagram below
A frequency distribution is shown below Class
Frequency
Lower class boundary 0.5
Class range
3
Upper class boundary 10.5
1–10 11–19
7
19.5
10.5
9
20–22
12
22.5
19.5
3
23–25
11
25.5
22.5
3
26–28
10
28.5
25.5
3
29–38
5
38.5
28.5
10
39–48
2
48.5
38.5
10
1344
10
Height of rectangle
3 = 0.3 10 7 = 0.78 9 12 =4 3 11 = 3.67 3 10 = 3.33 3 5 = 0.5 10 2 = 0.2 10
© 2014, John Bird
5. Form a cumulative frequency distribution and hence draw the ogive for the frequency distribution given in the solution to Problem 3.
A cumulative frequency distribution is shown below Class
Frequency
Upper class boundary Less than
Cumulative frequency
20.5–20.9
3
20.95
3
21.0–21.4
10
21.45
13
21.5–21.9
11
21.95
24
22.0–22.4
13
22.45
37
22.5–22.9
9
22.95
46
23.0–23.4
2
23.45
48
An ogive for the above frequency distribution is shown below
6. Draw a histogram for the frequency distribution given in the solution to Problem 4.
From the frequency distribution in Problem 4, the histogram is shown below
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© 2014, John Bird
7. The frequency distribution for a batch of 50 capacitors of similar value, measured in microfarads, is: 10.5–10.9
2,
11.0–11.4
7,
11.5–11.9
10,
12.0–12.4 12,
12.5–12.9
11,
13.0–13.4
8
Form a cumulative frequency distribution for these data.
A cumulative frequency distribution for the data is shown in the table below Class
Frequency
10.5–10.9
2
Upper class boundary less than 10.95
Cumulative frequency
11.0–11.4
7
11.45
9
11.5–11.9
10
11.95
19
12.0–12.4
12
12.45
31
12.5–12.9
11
12.95
42
13.0–13.4
8
13.45
50
2
8. Draw an ogive for the data given in the solution of Problem 7.
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© 2014, John Bird
An ogive, i.e. a graph of cumulative frequency against upper class boundary values, having coordinates given in the above answer to Problem 7, is shown below
9. The diameter in millimetres of a reel of wire is measured in 48 places and the results are as shown. 2.10
2.29
2.32
2.21
2.14
2.22
2.28
2.18
2.17
2.20
2.23
2.13
2.26
2.10
2.21
2.17
2.28
2.15
2.16
2.25
2.23
2.11
2.27
2.34
2.24
2.05
2.29
2.18
2.24
2.16
2.15
2.22
2.14
2.27
2.09
2.21
2.11
2.17
2.22
2.19
2.12
2.20
2.23
2.07
2.13
2.26
2.16
2.12
(a) Form a frequency distribution of diameters having about 6 classes. (b) Draw a histogram depicting the data. (c) Form a cumulative frequency distribution. (d) Draw an ogive for the data.
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© 2014, John Bird
(a) Range = 2.34–2.05 = 0.29 0.29 ÷ 6 ≈ 0.5, hence classes of 2.05–2.09, 2.10–2.14 and so on are chosen, as shown in the frequency distribution below
(b) A histogram depicting the data is shown below
(c) A cumulative frequency distribution is shown below
Class
Frequency
Upper class boundary Less than
Cumulative frequency
2.05–2.09
3
2.095
3
2.10–2.14
10
2.145
13
2.15–2.19
11
2.195
24
2.20–2.24
13
2.245
37
2.25–2.29
9
2.295
46
2.30–2.34
2
2.345
48
(d) An ogive for the above data is shown below 1348
© 2014, John Bird
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© 2014, John Bird
