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Solved Examples
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 D   Based on the histogram shown, what could be said about the weights of 200 fishes? The following are the observations drawn from the graph. Identify the incorrect observation.I. Weights of fishes are between 3 and 21 pounds.II. 60% of the fishes weighed between 9 and 18 pounds.III. 110 fishes weighed between 6 and 12 pounds.IV. 70% of the fishes weighed more than 12 pounds.   D View Solution
 D   A jewellery store sells gold chains, pendants and bracelets. The cost of 24 different gold bracelets (of the same weight) are \$150, \$100, \$150, \$200, \$150, \$100, \$150, \$100, \$150, \$100, \$150, \$100, \$150, \$100, \$150, \$200, \$100, \$150, \$150, \$100, \$150, \$200, \$150 and \$200. Make a frequency distribution for the data.   D View Solution
 D   A research scholar wants to complete the research work done by his student. In the data available with him, the class limits are missing. Find the class boundaries of each class whose midvalues are 25, 34, 43, 52, 61 and 70.   D View Solution
 D   Which of the following statement(s) is/are true?I. A Pareto chart is used for categorical data. II. An ogive is used to represent quantitative data.III. Pareto chart is used to represent the data collected over a period of time.   D View Solution
 D   Using the histogram, construct a frequency polygon.   D View Solution
 D   Edward took 16 mock tests. In 3 of the tests, his score is average. In 2 of the tests, his score is above average and in 5 of the tests his score is below average. In the remaining 6 tests his score is good. Which frequency distribution is appropriate for his test scores?   D View Solution
 D   Select the correct statements:I. Pie graph is the best representation to show the relationship between the parts and the whole.II. Pareto chart is used to show frequencies for nominal or qualitative variables.III. Frequency polygon is another name for ogive.   D View Solution
 D   Match data in Set A with corresponding data in Set B:   D View Solution
D   Mr. Craig made a frequency distribution for the scores secured by his students in a test.
 Score Number of students Below 75 9 76 - 80 19 81 - 85 3 86 - 90 5 91 - 95 3 96 - 100 1

How many students got more than 85 points?
D
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D   An animal trainer conducted some tests on different kinds of cats to study their reaction time (in seconds) to a specific stimulus.
 Reaction time Number of cats (frequency) 2.3 - 2.6 6 2.7 - 3.0 2 3.1 - 3.4 10 3.5 - 3.8 8 3.9 - 4.2 4 4.3 - 4.6 12

Which of the ogives represents the data obtained by the animal trainer?   D
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 D   Recognize the false statement(s).I. The numbers used to separate the classes, so that there are no gaps in the frequency distribution are called class limits.II. Class width for a class is found by subtracting the lower class limit from the upper class limit.III. Class midpoint is obtained by adding the lower and upper boundaries and dividing by 2.IV. The class limits should have the same decimal place value as the data, but the class boundaries should have one additional place value.   D View Solution
D   What type of distribution does the table represent?
 Age Below 10 10 - 20 21 - 31 32 - 42 43 - 53 54 - 64 65 and above

D
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D   The daily water consumption (in m3) of 25 different textile mills recorded by the Water Authority is shown.
 2400 2700 1100 1830 2200 2250 1400 1720 2620 1580 1640 2100 1360 1750 2600 1440 1900 2520 1700 1210 2300 2050 1500 1990 2320

Identify the frequency of each class by constructing a frequency distribution with six classes.   D
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 D   The amount of carbohydrates (in grams) contained in a variety of fast food items is shown. Identify the ogive which represents the data.   D View Solution
 D   The survey results of the ages of students in the Adult Basic Education Maths classes are shown in the bar graph. Find the median, lower quartile by constructing the ogive of the data.   D View Solution
 D   Age in years of twenty secondary school students visiting the zoo on a week day were recorded. The results were :12, 16, 10, 19, 17, 10, 10, 11, 11, 11, 11, 12, 12, 11, 12, 13, 12, 14, 15, 18Construct an ogive and find the median age and the interquartile range of ages.   D View Solution
D   The velocity (m/sec) of water flow in a pipe of 25 m diameter for consecutive days of a month are observed as:
 1.5 1.5 1.6 1.4 1.5 1.4 1.6 1.4 1.5 1.3 1.4 1.3 1.4 1.5 1.7 1.6 1.5 1.5 1.5 1.4 1.3 1.5 1.5 1.6 1.7 1.5 1.4 1.4 1.4 1.5

Find the class boundaries for the last class by constructing an ungrouped frequency distribution.
D
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D   The daily sales of books in a book stall for 20 consecutive days are:
 20 15 32 18 40 9 12 19 22 28 31 54 42 39 45 16 60 38 44 25

Find the class limit in which the sales are maximum by constructing a frequency distribution table with 5 classes.
D
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D   The HR manager for a company asked its employees to give the details about their residing places. The details obtained by him are categorized into places as recorded: A = Atkinson Square, C = Caribbean Point, D = Dream Valley, E = Environ Enclave, T = Township, M = Montessori Enclave.
 A T E C A M D A M M E C E M C M T T E D A M M T T

Which of the following tables represents the frequency distribution of the above data? From which place the employees are more?
D
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 D   The students of Environmental studies collected the data of the life span of Zebras from the zoological authorities which are as follows. 20, 12, 19, 22, 28, 30, 17, 25, 10, 23, 16, 18, 21, 32, 15, 14, 8, 22, 11, 13, 18, 20, 21, 19, 19 Find the average life span of a Zebra by constructing a frequency distribution table.   D View Solution
D   The distance traveled (in thousands of kilometers) by female drivers in an year is as recorded.
 Distance traveled Number of females (Frequency) 2 0 4 4 6 7 8 18 10 24 12 27 14 14 16 6

Construct a frequency polygon and find the mean.   D
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 D   Plant scientists developed different varieties of corns that have a rich content of lysine which is a nutritious animal feed. A group of chicks were given this food to test the quality. Weight gains (in grams) of these chicks after 21 days are as recorded: 380, 321, 366, 356, 349, 337, 399, 384, 410, 329, 350, 340, 324, 396, 412, 420, 382, 318, 344, 438. By constructing a frequency distribution table for 7 classes, find the class interval in which the weight increase is maximum.   D View Solution
 D   Which among the following statement(s) is/are true about histograms?I. Midpoints are useful in determining class widths and class boundaries.II. Histograms are useful in displaying cumulative frequencies.III. Histograms are used to display categorical data.IV. Histograms are not used to represent continuous data.   D View Solution
D   The frequency distrubution table shown here is incorrectly constructed. State the reason.
 Class Frequency 7 - 12 3 13 - 18 1 19 - 24 4 25 - 30 6 31 - 36 2

D
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 D   Which of the following statement(s) is/are not true about histograms?I. The bars must touch each other.II. The width of each class must be same.III. A histogram for a given set of data may be symmetric or skewed depending on the selection of class width and boundaries.IV. Histograms should not have gaps and clusters.   D View Solution
D   Identify the discrepancy in the frequency distribution.
 Class Frequency 15 - 19 2 19 - 23 3 23 - 27 1 27 - 31 6 31 - 35 4

D
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D   Identify the error in constructing frequency distribution table.
 Class Frequency 53 - 57 8 58 - 62 4 68 - 71 3 72 - 77 1

D
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D   A frequency distribution of the duration of telephone calls monitored at the local telephone exchange are shown.
 Length of calls(minutes) Number of calls 2.5 - 4.5 10 4.5 - 6.5 15 6.5 - 8.5 30 8.5 - 10.5 15
Construct a frequency polygon and ogive for the data.
D
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D   The frequencies of ages of freshmen(fresh students) at a private university are as recorded.
 Age Range Percentage of Enrolment 18 - 20 40 20 - 22 25 22 - 24 15 24 - 26 20
Construct an ogive and a histogram for the data.
D
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ee  Harrison goes for daily morning walk. The number of rounds walked by him around a park per day for a period of one month is recorded. Construct a frequency distribution table for this data.
 2 4 3 5 2 1 3 2 3 4 6 2 1 3 4 3 3 2 2 4 5 6 3 4 3 2 5 4 3 3
ee
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 ee  Identify the incorrect statement.I. The histogram is a graph that displays the data by using continuous vertical bars of various heights to represent the frequencies of classes.II. The frequency polygon is a graph that displays the data by using lines that connect points plotted for the frequencies of the midpoint of the classes. The frequencies are represented by the heights of the points.III. The ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution.IV. For any given dataset, all the three graphs (histogram, frequency polygon and ogive) can be drawn.  ee View Solution
ee  The rainfall per day at a place (in mm) is recorded for 50 days.
 Rainfall (in mm) No. of days 1 - 4 4 5 - 8 6 9 - 12 10 13 - 16 14 17 - 20 7 21 - 24 4 25 - 28 3 29 - 32 2
Select the appropriate graph / graphs representing the ogive.
ee
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 ee  Identify the statement which does not form a part of the procedure in the construction of a frequency table.I. The number of classes should be between 6 and 20.II. The class width should be an even number.III. The classes must be mutually exclusive.IV. The classes must be continuous.V. The classes must be exhaustive.VI. The classes must be equal in width.  ee View Solution
 ee  Which of the following statement(s) is/are true?I. The other name for an ogive is a frequency polygon.II. The boundaries for the class limits 8.6 - 8.8 are 8.55 - 8.85.III. A Pareto chart can be used to show the relationship between the parts and the whole.  ee View Solution
 ee  Which of the following statement(s) is/are true?I. On a pareto chart, the frequencies should be represented on the y - axis.II. In a frequency distribution, the number of classes should be between 5 and 20.III. The three types of frequency distributions are histograms, frequency polygons and ogives.  ee View Solution
 ee  Which of the following statement(s) is/are false?I. Data such as blood types (A, B, AB, O) can be organised into a categorical frequency distribution.II. Except for rounding errors, relative frequencies should add up to 100.III. A statistical device used in exploratory data analysis which is a combination of a frequency distribution and a histogram is called stem and leaf plot.  ee View Solution
ee  A survey of 50 clothing stores reported these number of sales held during a randomly selected month. Select the correct histogram representing the data shown.
 Number of sales Frequency 11 - 15 5 16 - 20 7 21 - 25 17 26 - 30 10 31 - 35 3 36 - 40 8

ee
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ee  Select the correct histogram representing the fuel capacity (in gallons) of 30 randomly selected cars in 1999.
 Fuel Capacity Number of cars 10 - 12 6 13 - 15 4 16 - 18 4 19 - 21 5 22 - 24 8 25 - 27 2 28 - 30 1
ee
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 ee  The histogram shows the number of hurricanes reaching the east coast of the United States each year over a period of 70 years. Describe the shape of this distribution and find the center of the distribution.  ee View Solution
ee  The frequency distribution for the systolic blood pressure readings (in millimeters of mercury - mm Hg) of 200 randomly selected college students is given.
 Systolic blood pressure reading Number of students 89.5 - 104.5 24 104.5 - 119.5 62 119.5 - 134.5 72 134.5 - 149.5 26 149.5 - 164.5 12 164.5 - 179.5 4

Which graph represents the frequency polygon of the given data?  ee
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ee  A statistics instructor wishes to see whether there is any relationship between the number of home work problems a student completes and his/her exam scores. The data is given as:
 Home work problems Exam score 6 65 8 71 10 75 12 98 14 93 16 63 18 72 20 89 22 100
Identify the frequency polygon which represents the relationship between home work problems solved and exam scores obtained.  ee
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ee  The airborne speeds (in miles per hour) of 21 planes are shown. Identify the frequency polygon that represents the data.
 Speed (in miles per hour) Number of planes (Frequency) 366 - 386 4 387 - 407 2 408 - 428 3 429 - 449 2 450 - 470 1 471 - 491 2 492 - 512 3 513 - 533 4
ee
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 ee  Name the graph shown.  ee View Solution
ee  The percent of words of 1 to 10 letters used in articles in popular fiction story book is recorded as shown.
 Length 1 2 3 4 5 6 7 8 9 10 Percent 3.6 14.8 18.7 16 12.5 8.2 8.1 5.9 4.4 2.1
Describe the shape of the distribution.
ee
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ee  The speed of an automobile (in miles per hour) and the corresponding mileage (in miles per gallon) is shown.
 Speed 20 30 40 50 60 Mileage 24 28 30 28 24
Describe the shape of the distribution.  ee
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ee  The typing speed (in words per minute) of 31 office assistants is shown.
 Typing speed Number of office assistants 54 - 58 2 59 - 63 5 64 - 68 8 69 - 73 6 74 - 78 4 79 - 83 5 84 - 88 1
Which frequency polygon represents the data?  ee
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ee  The cost per load (in cents) of 35 laundry detergents used by a consumer organization are given.
 Cost per load Number of detergents 13 - 19 2 20 - 26 7 27 - 33 12 34 - 40 5 41 - 47 6 48 - 54 1 55 - 61 0 62 - 68 2
Which graph represents the frequency polygon for the given data?
ee
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ee  The frequency distribution represents the data obtained from a sample of computer repairs. The values are the mean time (in hours) between repairs on 80 machines.
 Mean time between repairs Number of machines 25.5 - 28.5 5 28.5 - 31.5 9 31.5 - 34.5 32 34.5 - 37.5 20 37.5 - 40.5 12 40.5 - 43.5 2
Which frequency polygon represents the given data?  ee
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ee  In an experiment the concrete blocks are tested for its withstanding capacity against corossion in a solution of hydrochloric acid. The reaction time (in seconds) are as recorded.
 Reaction time (in seconds) Number of blocks 2.1 - 2.7 12 2.8 - 3.4 13 3.5 - 4.1 7 4.2 - 4.8 5 4.9 - 5.5 2 5.6 - 6.2 1
Which ogive represents the data?  ee
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 ee  Ms. Clara, the class teacher of 8th Grade prepared a record of the students and the country of their origin. The recordings are given. Find the percentage of students with country of origin as West Indies and South America.  ee View Solution
ee  The weekly wages of 65 employees at ABC company are recorded and a frequency distribution table is prepared.
 Wages (\$) Number of employees 250 - 259.99 8 260 - 269.99 10 270 - 279.99 16 280 - 289.99 14 290 - 299.99 10 300 - 309.99 5 310 - 319.99 2

Find
(i). The percentage of employees earning less than \$280.00 per week.
(ii). The percentage of employees earning less than \$300 per week but at least \$260.00 per week.  ee
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ee  The frequency distribution for the time (in minutes) spent per day on the computer by 400 employees in a company is shown.
I. Find the percentage of employees who spend atmost 600 minutes per day on computer.
II. Find the percentage of employees who spend atleast 500 minutes but less than 1000 minutes.
III. Find the time interval in which maximum number of employees spend before the computer.
 Time (minutes) Number of employees 300 - 399 14 400 - 499 46 500 - 599 58 600 - 699 76 700 - 799 68 800 - 899 62 900 - 999 48 1000 - 1099 22 1100 - 1199 6
ee
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