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Solved Examples
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BB  Which of the box plots represent the Richter magnitudes of 5 earthquakes if their Richter magnitudes are given as 6.4, 6.2, 5.4, 7.7 and 8.0?
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BB  The cumulative frequency for the distribution of the distance (in miles) that 20 randomly selected runners ran during a week is given in the ogive. Find the interquartile range for the data by constructing a box plot.  BB View Solution
BB  Interpret the ogive of temperatures (°F) recorded at 50 different places. Identify the five number summary of this data from the graph.
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BB  Identify the five-number summary for the number of previous jobs held by each of six job applicants for clerk's post to BRR company if the number of jobs data is given as 2, 4, 5, 6, 8, 9.
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BB  The box plot shown represents five number summary of the stopping distance (in feet) of 9 different automobiles after applying brakes, travelling at a speed of 15 miles per hour. Find the maximum distance, minimum distance and interquartile range.
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BB  Which of the following box plots represents the number of calculators sold during a randomly selected week?
8, 12, 23, 5, 9, 15, 3.
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BB  P50 corresponds to ____.
I. Q2
II. IQR
III. MR
IV. D5
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BB  Which is not part of the five-number summary?
I. Q1 and Q3
II. The mean
III. The median
IV. The smallest and largest data values  BB
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BB  The box plot represents the five-number summary of the temperatures recorded at a particular place in California state for the first week of April 2003. The recorded temperatures in °F are 87, 85, 80, 78, 83, 86, 90. Find maximum temperature, minimum temperature and interquartile range.
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BB  Which of the following statement(s) can be inferred from a box plot?
I. In a box plot, if the median falls to the left of the center of the box, then the distribution is negatively skewed.
II. If the median is near the center of the box, the distribution is approximately symmetric.
III. If the lines outside the box are about the same length, the distribution is positively skewed.
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BB  Identify the incorrect statement(s).
I. Percentiles divide the data set into 100 equal groups.
II. Deciles divide the distribution into 10 equal groups.
III. Quartiles divide the distribution into 25 equal groups.  BB
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BB  Recognize the incorrect statement(s).
I. When all data for a variable are transformed into z scores, the resulting distribution will have a mean of 1 and a standard deviation of 0.
II. The z score represents the number of standard deviations that a data value falls above or below the mean.
III. Percentages are position measures used to compare the relative position of an individual in a group.
IV. Percentile divide the data set into 100 equal groups.  BB
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BB  The owner of a restaurant recorded the number of visitors for a period of one week. Examine the nature of distribution of the data, using a box plot. 256, 542, 340, 460, 380, 429, 412
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BB  The time (in minutes) taken by Moore and James to swim 2000 yards for 8 sessions in a pool are given.
MooreJames
34.0236.12
34.1235.37
35.7235.57
34.7235.43
34.0536.05
34.1334.85
36.1734.75
36.0734.18
Compare the distributions using box plots.  BB
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BB  The median price of different books in a bookstall is $35.The difference between twice the minimum price and half the maximum price in the bookstall gives the median price, which is also equal to the midrange. The IQR of the prices is $5. The price of the book corresponding to 25th percentile is $32. Identify five - number summary .
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BB  An automobile company is interested in comparing the car models launched in the market in 1998 and 1999. The fuel consumption (in miles per gallon) of different models are given in the table.
Car ModelsFuel consumption in the year 1998Fuel consumption in the year 1999
A1916
B2019
C1817
D1618
E2221
F2420
Compare the data. The car models of which year has less fuel consumption?  BB
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BB  The percentage of points scored by Jack each year during his four year degree course is shown in the table. Which is the equivalent box-and-whisker plot for the data? Also find the average percentage of points scored by him during the course.
YearPercentage of points
1st Year70
2nd Year82
3rd Year76
4th Year80

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BB  The scoreboard of a 100 meters running race is shown here. Construct a box-and-whisker plot for the data shown in the table. Also find out the range of the box-and-whisker plot.
ContestantTime taken (in seconds)
Tony20
James18
Joe14
Louis10
Peter18
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BB  The owner of a super market recorded the number of customers visiting his store per hour in a day. The results were 15, 10, 12, 9, 18, 5, 8, 9, 15, 10 and 11. Construct a box plot for the data.  BB View Solution
BB  A recent survey by a broadcasting company revealed that the number of viewers of different T.V channels in U.S.A are as recorded. Choose the appropriate box-and-whisker plot for the data and find the mean number of T.V viewers.
Number of viewers of different T.V channels in U.S
ChannelNumber of viewers (in millions)
Discovery20
HBO32
Fox Sports10
CNN14
Cartoon Network16
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BB  The expenditure of Jennifer in a day is as recorded in the table. Which box-and-whisker plot represents the data in the table?
ItemExpenditure ($)
Food products6.50
Perfumes6.00
Souvenirs1.00
Cosmetics3.50
Accessories2.50
Leather items7.00
Other items0.50

What is the product of all the three quartiles of the box-and-whisker plot?  BB
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BB  The approximate height (in hundred feet) of mountains in U.S are shown in the table. Choose the appropriate box-and-whisker plot for the data and find the mean height of the mountains in U.S.
NameHeight (in hundred ft.)
Mt. McKinley200
Mt. St. Elias180
Mt. Foraker175
Mt. Bona165
Mt. Blackburn160
Mt. Alverstone145
Sunshine Peak140

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BB  What is the outlier in the box-and-whisker plot?  BB View Solution
BB  Which of the following statement(s) is/are true?
I. If a student secured 75th percentile in an exam, then it means that he scored 75 out of 100.
II. A statistic that tells the number of standard deviations a data value is above or below the mean is called z score.
III. The distribution is positively skewed if the mode is to the left of the median and the mean is to the right of the median.  BB
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BB  Which of the following statement(s) is/are true ?
I. Mode is the measure of central tendency used in exploratory data analysis (EDA).
II. Extremely low data value in the data set can be considered as an outlier.
III. Percentiles are the same as percentages.  BB
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BB  What is the percentage of the box in the box-and-whisker plot?  BB View Solution