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| f If the mean of seven values is 108. Find the sum of the values. f |
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f Find the mean of 5, 10, 15, 20, 25 and 30. Increase each value by 15 and find the mean of the new data. Are the two means the same?
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f The time (in minutes) taken by 10 students to complete a statistics test was 15, 10, 12, 7, 9, 13, 15, 6, 14, 8. Find the midrange and comment on the skewness of the distribution.
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| f The number of years served by 9 Prime Ministers of a country are 3, 5, 4, 6, 2, 7, 8, 1 and 10. Find the median and the midrange of the above data. Are they equal? f |
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f A sales person drives 200 miles round trip at 25 mph going to California and 40 mph returning home. Find the average speed.
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f Which of the following statement(s) is/are true?
I. The mode for the traffic fatalities for 10 selected states in a specific year (1488, 1586, 4192, 1031, 645, 74, 158, 875, 3360, 325) is zero.
II. The mode is not always unique for a data set.
III. The midrange of 2, 3, 6, 8, 4, 1 is 3.5.
IV. The midrange and median for the data in statement III are same.
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f The salaries for the staff of ABC automobile company are shown here. The mean of the salaries is $27,500. Find the salary of the sales executive. | Staff | Salary ($) | | Owner | 80000 | | Manager | 35000 | | Sales Manager | 30000 | | Sales executive | _______ | | Worker 1 | 10000 | | Worker 2 | 7000 | | Worker 3 | 8500 |
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f Which of the following statement(s) is/are true?
I. The population mean is represented by the Roman letter X¯. The sample mean is represented by the Greek letter μ.
II. The measures that determine the spread of the data values are called measures of dispersion.
III. The ages of middle school children whose median age is 10 years are all below 10 years.
IV. The mean of the salaries of all the employees working in a small company is represented by μ.
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f In a business meeting, the General Manager (GM) of a company stated that his employees had an average service of 9 years. Later, the Assistant Manager found the statement delivered by the GM was incorrect after verifying the data shown.| No.of employees (X) | Years of service (w) | | 8 | 2 | | 2 | 6 | | 3 | 10 |
Find the correct weighted mean service of employees.
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f The number of ATM transactions of a particular bank recorded at 12 locations in a city on a day are as follows.
24, 42, 210, 69, 38, 72, 59, 44, 96, 21, 318, 66
Find the median and mean of the number of transactions. Which is greater, median or mean?
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| f A car travels a distance of first 15 miles at a speed of 15 mph, next 15 miles at 30 mph and another 15 miles at 45 mph. Find the arithmetic mean and harmonic mean of these 3 speeds. Which is the correct measure of average speed? f |
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f Which of the following statement(s) is/are true ?
I. If the mean of the given data set 3, 6, 12, ___ is 9, then the missing number is 12.
II. If the mode of the given data set 1, 0, 2, 5, 9, 11, 13, 14, 7, ___ is 0, then the missing number is 3.
III. If the median of 2, 3, 11, 1, 6, 14, ___ , 8, 9 is 8, then the missing number is greater than 8.
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f Three cities A, B and C are equidistant from each other. A motorist travels from A to B at 30 km/hr, from B to C at 40 km/hr, from C to A at 50 km/hr. Determine the average speed.
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f A box contains balls numbered 1 through 8. The ball drawn from the box is replaced after noting the number. The numbers so obtained are: 3, 5, 8, 1, 2, 5, 1, 2, 1, 5, 4, 1, 7, 5, and 8.
Find the mode of the numbers.
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f The data represents the percentage of children suffering from vascular diseases in 8 selected areas of 2 different countries. Find the mean, median, mode and midrange for country 1 and country 2.
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| f What is the empirical relation between mean, median and mode? f |
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f A recent survey of different companies reported the following percentages of people working in night shifts. Find the weighted mean of percentages.| Company | % of people working in night shifts (w) | Number of people surveyed (X) | | 1 | 15 | 200 | | 2 | 22 | 150 | | 3 | 18 | 180 | | 4 | 30 | 220 | | 5 | 25 | 300 |
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f Identify the incorrect statement(s).
I. For an open-ended frequency distribution, Mean is the best average.
II. Mean and Midrange are not effected by extremely high or low values in a data set.
III. Bimodal is a data set with two modes.
IV. Mode is the easiest average to compute.
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f Describe which measure of central tendency - mean, median, or mode was probably used in each situation. Answer in order.
I. One half of the gross domestic product (GDP) of country A comes from more than 42.5% of its citizens.
II. Computation of per-capita income in several countries.
III. A person on an average eats sea food once a week.
IV. Average sales of a company for various years.
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f A recent survey of a TV channel reported the percentage of viewers for different programs in a state. Find the mean percentage.| Program | Viewers (%) | | 1 | 12 | | 2 | 2.83 | | 3 | 56.7 | | 4 | 1 | | 5 | 18.66 |
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f Identify the incorrect statement.
I. Mean is the sum of values divided by the total number of values.
II. Median is the middle point in data set that has been ordered.
III. Mode is the highest value in the data set.
IV. Midrange is the difference between the highest value and the lowest value. f |
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| f Find the arithmetic mean of the first n natural numbers. f |
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f Identify the incorrect statement(s).
I. Mean is the most stable measure of central tendency.
II. If the mean of a set of 6 observations is 8 and the mean of a set of 4 observations is 9, then the mean for the combined set of observations is 8.4.
III. To compare the heights of the students in a class, the most suitable measure of central tendency is Median.
IV. Mode is the average suited for open ended classes. f |
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| f The height (in feet) of 5 students of a class are recorded as 4.2, 5, 4.6, 5.1 and 4.8. What is the mean height? f |
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f Time taken by each worker to complete a piece of work is recorded here. Find the mean time.| Name | Time (in hours) | | John | 44 | | David | 38 | | Mike | 42 | | Stephen | 39 | | Joseph | 36 | | Steve | 41 |
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f 8 concrete blocks were tested in a lab to determine the crushing strength of concrete. The crushing strength of block E was missing from the final records. But the mean crushing strength was recorded as 4.45 tonnes/cm2. What was the measured crushing strength of block E?| Block | Crushing strength (tonnes/cm2) | | A | 4.8 | | B | 4.2 | | C | 5.1 | | D | 3.8 | | E | __ | | F | 4.7 | | G | 4.1 | | H | 4.5 |
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| f Johnny read 9, 14, 12, 25, 18, 30, 4 and 22 pages of the latest fiction book he took from the school library for 8 consecutive days. Find the median of the pages he read. f |
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f The number of points scored by the captain in the first 10 minutes of 15 matches in a basketball tournament are: 5, 4, 6, 5, 2, 8, 8, 5, 5, 3, 5, 4, 1, 4 and 6. What is the mode of the data?
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f Find the mode for the following data. The data represents the number of vehicles passing through a point on a highway per hour:
130, 86, 79, 114, 91, 49, 63, 59, 81, 57
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| f Find the average percentage raise of salary if a person receives 25% raise after 1 year of service and 15% raise after the second year of service. f |
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f Recognize the incorrect statement(s).
I. A distribution having only one mode is called unimodal.
II. The class with largest frequency is called model class.
III. The price of bread packet for 7 consecutive years is $2.00, $2.20, $2.70, $3.00, $3.10, $3.60, $3.90. The mode of the given data is zero.
IV. The ordered data set is called data array.
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f The number of toys sold in a shop per day for 10 days are as follows.
21, 33, 18, 15, 28, 11, 19, 28, 14, 30
Find the midrange of the data set. f |
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