Consider the following dataset.
`{:[13,16,17,17,21,24]:}`
Which row of the table shows how the median and mean are affected when a score of 5 is added to the dataset?
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Consider the following dataset.
`{:[13,16,17,17,21,24]:}`
Which row of the table shows how the median and mean are affected when a score of 5 is added to the dataset?
`D`
`text{Mean decreases.}`
`text{Median remains 17.}`
`=>D`
Vicki wants to investigate the number of hours spent on homework by students at her high school.
She asks each student how many hours (to the nearest hour) they usually spend on homework during one week.
The responses are shown in the frequency table.
What is the mean amount of time spent on homework? (2 marks)
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`text(7.275 hours)`
`text(Mean)` | `= text(Sum of Scores) / text(Total scores)` |
`= 1455/200` | |
`= 7.275\ text(hours)` |
A small population consists of three students of heights 153 cm, 168 cm and 174 cm. Samples of varying sizes can be taken from this population.
What is the mean of the mean heights of all the possible samples? Justify your answer. (2 marks)
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`165\ text(cm)`
`text(If sample is 1 person,)`
`text{Possible mean(s): 153, 168 or 174.}`
`text(If sample is 2 people,)`
`text{Possible mean(s):}quad(153 + 168)/2` | `= 160.5` |
`(153 + 174)/2` | `= 163.5` |
`(168 + 174)/2` | `= 171` |
`text(If sample is 3 people,)`
`text(Mean:)quad(153 + 168 + 174)/3 = 165`
`:.\ text(Mean of all mean heights)`
`= (153 + 168 + 174 + 160.5 + 163.5 + 171 + 165)/7`
`= 165\ text(cm)`
A grouped data frequency table is shown.
What is the mean for this set of data?
(A) 6.5
(B) 10.5
(C) 11.9
(D) 12.4
`=> D`
`text(Using the centre of each class interval:)`
`text(Mean)` | `= (3 xx 3 + 8 xx 6 + 13 xx 8 + 18 xx 9)/(3 + 6 + 8 + 9)` |
`= 12.42…` |
`=> D`
The mean of a set of 5 scores is 62.
What is the new mean of the set of scores after a score of 14 is added?
(A) 38
(B) 54
(C) 62
(D) 76
`B`
`text(Mean of 5 scores) = 62`
`:.\ text(Total of 5 scores) = 62 xx 5 = 310`
`text(Add a score of 14)`
`text(Total of 6 scores) = 310 + 14 = 324`
`:.\ text(New mean)` | `= 324/6` |
`= 54` |
`=> B`
Consider the following set of scores:
`3, \ 5, \ 5, \ 6, \ 8, \ 8, \ 9, \ 10, \ 10, \ 50.`
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`text(would become lower.)`
`text(Median will NOT change.)`
i. `text(Total of scores)`
`= 3 + 5 + 5 + 6 + 8 + 8 + 9 + 10 + 10 +50`
`= 114`
`:.\ text(Mean) = 114/10 = 11.4`
ii. `text(Mean)`
`text{If the outlier (50) is removed, the mean}`
`text(would become lower.)`
`text(Median)`
`text(The current median (10 data points))`
`= text(5th + 6th)/2 = (8 + 8)/2 = 8`
`text(The new median (9 data points))`
`=\ text(5th value)`
`= 8`
`:.\ text(Median will NOT change.)`
Christina has completed three Mathematics tests. Her mean mark is 72%.
What mark (out of 100) does she have to get in her next test to increase her mean mark to 73%? (2 marks)
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`76`
`text(Total marks in 3 tests)`
`= 3 xx 72`
`= 216`
`text(We need 4-test mean) = 73`
`text(i.e.)\ \ \ ` | `text{Total Marks (4 tests)}-:4` | `= 73` |
`text(Total Marks)\ text{(4 tests)}` | `= 292` |
`:.\ text(4th test score)` | `= 292 – 216` |
`= 76` |
The height of each student in a class was measured and it was found that the mean height was 160 cm.
Two students were absent. When their heights were included in the data for the class, the mean height did not change.
Which of the following heights are possible for the two absent students?
(A) 155 cm and 162 cm
(B) 152 cm and 167 cm
(C) 149 cm and 171 cm
(D) 143 cm and 178 cm
`C`
`text(S) text(ince the mean doesn’t change)`
`=>\ text(2 absent students must have a)`
`text(mean height of 160 cm.)`
`text(Considering each option given,)`
`(149 + 171) -: 2 = 160`
`=> C`
Twenty Year 12 students were surveyed. These students were asked how many hours of sport they play per week, to the nearest hour.
The results are shown in the frequency table.
What is the mean number of hours of sport played by the students per week?
(A) 3.3
(B) 4.3
(C) 5.0
(D) 5.3
`B`
`text(Using the class centres)`
`text(Total hours)` | `= (1 xx 5) + (4 xx 10) + (7 xx 3) + (10 xx 2)` |
`= 5 + 40 + 21 + 20` | |
`= 86` |
`text(Mean hours)` | `= 86/20 = 4.3` |
`=> B`
The heights of the players in a basketball team were recorded as 1.8 m, 1.83 m, 1.84 m, 1.86 m and 1.92 m. When a sixth player joined the team, the average height of the players increased by 1 centimetre.
What was the height of the sixth player?
(A) 1.85 m
(B) 1.86 m
(C) 1.91 m
(D) 1.93 m
`C`
`text(Old Mean)` | `=(1.8+1.83+1.84+1.86+1.92)-:5` |
`=9.25/5` | |
`=1.85\ \ text(m)` |
`text{S}text{ince the new mean = 1.86m (given)}`
`text(New Mean)` | `=text(Height of all 6 players) -: 6` |
`:.1.86` | `=(9.25+h)/6\ \ \ \ (h\ text{= height of new player})` |
`h` | `=(6xx1.86)-9.25` |
`=1.91\ \ text(m)` |
`=> C`
The eye colours of a sample of children were recorded.
When analysing this data, which of the following could be found?
`C`
`text(Eye colour is categorical data)`
`:.\ text(Only the mode can be found)`
`=> C`
The mean of a set of ten scores is 14. Another two scores are included and the new mean is 16.
What is the mean of the two additional scores?
(A) 4
(B) 16
(C) 18
(D) 26
`D`
`text(If ) bar x\ text(of 10 scores = 14)`
`=>text(Sum of 10 scores)= 10 xx 14 = 140`
`text(With 2 additional scores,)\ \ bar x = 16 `
`=>text(Sum of 12 scores)= 12 xx 16 = 192`
`:.\ text(Value of 2 extra scores)` | `= 192\-140` |
`= 52` |
`:.\ text(Mean of 2 extra scores)= 52/2 = 26`
`=> D`
The July sales prices for properties in a suburb were:
$552 000, $595 000, $607 000, $607 000, $682 000, and $685 000.
On 1 August, another property in the same suburb was sold for over one million dollars.
If the property had been sold in July, what effect would it have had on the mean and median sale prices for July?
(A) Both the mean and median would have changed.
(B) Neither the mean nor the median would have changed.
(C) The mean would have changed and the median would have stayed the same.
(D) The mean would have stayed the same and the median would have changed.
`C`
`text(Mean increases because new house is sold above)`
`text(the existing average.)`
`text(Initial median)= (607\ 000+607\ 000)/2=607\ 000`
`text(New median)=607\ 000\ \ \ text{(4th value in a list of 7)}`
`=>\ C`