TopicName Test - Jacaranda



WorkSHEET 10.2 Describing, exploring and comparing data

Name: ___________________________

| |The following data show the survey results of the number of children | | |

| |in families. |[pic] | |

| | | | |

| |Data: | | |

| |3, 5, 2, 4, 3, 1, 4, 1, 2, 5, 3, 6, 4, 3, 5, 4, 4. | | |

| | | | |

| |Create a frequency table for this data. | | |

| | | | |

| | | | |

| | | | |

| |Using the frequency table from question 1 find: | | |

| | |[pic] | |

| |the mean number of children per family |[pic] | |

| | | | |

| |the median number of children per family |1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, | |

| | |Median = 4 | |

| |the modal number of children per family | | |

| | |Mode = 4 | |

| | | | |

| |Lachlan has calculated his mean mathematics score to be 67%, based on |[pic] | |

| |eight tests. If he scores 75% on the ninth test, what will his new | | |

| |mean score be? |Lachlan’s new mean score will be 68%. | |

| | | | |

| |A shoe company surveyed the shoe size purchased by women over a period| |

| |of time. | |

| |The results were as follows: |[pic] |

| | |The mean shoe size is 7. |

| |8, 5, 6, 5, 8, 6, 7, 9, 5, 7, 6, 8, 8, 6, 9, 7, and 8. | |

| | |The mode is 8 |

| |Calculate the mean of this data | |

| |Find the modal value. |5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, |

| |Find the median value. |The median value is 7. |

| |Which of these values would be of the most use to the company? Why? | |

| | |The mode would probably be of the most value because this is the shoe size |

| | |that they sell the most. |

| | | |

| |Tom has been earning some extra pocket money by washing cars. |[pic] | |

| |In each hour block he has managed to wash 4 cars, 5 cars, 3 cars, 4 |Tom needs to wash 10 cars in his next hour. | |

| |cars and 4 cars. |No, this is not very likely. | |

| |The mean number of cars that he has been able to wash is therefore 4 | | |

| |cars per hour. | | |

| |In order to increase his mean to 5 cars per hour, how many cars does | | |

| |Tom need to wash in the next hour? Is this likely? | | |

| | | | |

| |This grouped frequency table gives the number of ‘salmon cod’ caught | |4 |

| |by a fisherman on 25 fishing trips. |[pic] | |

| | | | |

| |[pic] |[pic] | |

| | | | |

| |Add a cumulative frequency column to the table, then use this to | | |

| |determine the median class. | | |

| | | | |

| |Use the frequency distribution table in questions 6 to calculate the | | |

| |mean number of ‘salmon cod’ caught by the fisherman on his 25 fishing |[pic] | |

| |trips. | | |

| | |[pic] | |

| | | | |

| | | | |

| |From the distribution table in question 6, determine the modal class. |modal class = 45 – 49 cod. | |

| |The number of goals scored by a team is shown below: | |2 |

| |5, 4, 4, 7, 5, 9, 12, 14, 16, 16. |4, 4, 5, 5, 7, 9, 12, 14, 16, 16 | |

| | | | |

| |Find the lower quartile. |LQ median UQ | |

| |Find the upper quartile. | | |

| |Find the interquartile range. |Lower quartile = 5 | |

| | |Upper quartile = 14 | |

| | |Interquartile range = 14 ( 5 | |

| | |= 9 | |

| |Use your calculator to find the standard deviation of the set of | |1 |

| |outcomes when a |Standard deviation = 1.87 | |

| |six-sided die is rolled as shown below. | | |

| | | | |

| |1, 2, 3, 4, 5, 6 | | |

| | | | |

| |State your answer correct to two decimal places. | | |

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