Worksheet 4.1Measures of Central Tendency
Maths Quest Maths A Year 12 for QueenslandChapter 4 Populations, samples, statistics and probability
WorkSHEET 4.11
WorkSHEET 4.1Measures of central tendency
Name: ______
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1 / For the set of test marks1, 4, 3, 5, 2, 7, 9, 9, 9, 10
determine:
(a)the mean
(b)the median
(c)the mode. /
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2 / For the set of test marks in question 1 determine:
(a)the range
(b)the interquartile range
(c)the standard deviation. /
(c)Enter the scores into a calculator and use the statistic function to determine the standard deviation.
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3 / Calculate the 5-number summary values for the mid-semester and end-semester tests for the 15 students in the table below.
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4 / A large block of land had an old cottage situated in one corner. The land was subdivided into six smaller blocks of land with the cottage sitting on one of them.
The cottage was valued at $65000. New houses were built on the other five blocks of land and they were valued at $165000, $200000, $185000, $200000 and $170000.
The value of the cottage would be regarded as an outlier compared with the values of the other five houses.
(a)Considering only the values of the five new houses, calculate the:
(i)mean
(ii)median
(iii)mode.
(b)Including the value of the cottage, calculate the:
(i)mean
(ii)median
(iii)mode.
(c)Comment on the effect the outlier has on these three measures. /
(c)
As can be seen from the table above, the inclusion of the value of the cottage has caused the mean to drop almost $20000. The median has only dropped $7500 and the modal value has not been affected by the outlier. / 6
5 / A basketball squad has eight players whose heights (in metres) are:
1.7, 1.82, 1.84, 1.85, 1.86, 1.86, 1.92.
The shortest player is injured. The substitute is 1.85mtall.
(a)What effect does this substitution have on the:
(i)mean
(ii)standard deviation of the players’
heights?
(b)Comment on any changes in these values. / (a) (i) and (ii)
(b)The mean has increased slightly because of the substitution of a taller player (1.85m for 1.7m). The standard deviation has decreased, showing that there is less variability in the height of the players. / 4
6 / The following contingency table summarises the composition of males and females employed by a bus driving company.
Calculate:
(a)the percentage of females who are drivers
(b)the percentage of drivers who are female. /
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7 / The following frequency histogram displays the distribution of a set of scores on a mental arithmetic test.
(a)Is the graph symmetrical?
(b)Is/are any mode(s) displayed here?
(c)Is it possible to determine the mean and median for this distribution? If so, what are their values? / (a)The graph is symmetrical.
(b)The scores(s) with the highest frequency is the mode.
In this case, there are two modes — 6 and8.
(c)Because the distribution is symmetrical, the mean and median will both be at the centre.
Mean = 7
Median = 7 / 3
8 / The ages of the 50 passengers on a bus are shown below. / (a)
(b)Total number less than
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(a)Represent the data as a frequency histogram.
(b)If one person from the bus was selected, what would be the probability that this person would be less than 30 years old?
9 / The following table records the number of people in a plant who did NOT have an accident over a 10-day period.
(a)Plot the scatterplot and draw the line of best fit.
(b)Use the line of best fit to predict the number of accident-free people on day 14 assuming that this trend continues. / (a)
(b)About 480 accident-free people are predicted. / 5
10 / The number of blue-eyed students in a mixed class of 30 students is shown in the contingency table below.
It was claimed that 25% of the male students in the class had blue eyes. Is this claim true? /
The claim that 25% of the male students in the class had blue eyes is NOT true. / 4