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UNIT 11 - IB Packet Name: _________________

1. The table below shows the frequency distribution of the number of dental fillings for a group of 25 children.

|Number of fillings |0 |1 |2 |3 |4 |5 |

|Frequency |4 |3 |8 |q |4 |1 |

(a) Find the value of q.

(2)

(b) Use your graphic display calculator to find

(i) the mean number of fillings;

(ii) the median number of fillings;

(iii) the standard deviation of the number of fillings.

(4)

(Total 6 marks)

2. 56 students were given a test out of 40 marks. The teacher used the following box and whisker plot to represent the marks of the students.

[pic]

(a) Write down

(i) the median mark;

(ii) the 75th percentile mark;

(iii) the range of marks.

(4)

(b) Estimate the number of students who achieved a mark greater than 32.

(2)

(Total 6 marks)

3. 31 pupils in a class were asked to estimate the number of sweets in a jar.

The following stem and leaf diagram gives their estimates.

|Stem |Leaf |

|4 |2, 4, 7, 8, 9 |

|5 |1, 1, 2, 3, 8, 9 |

|6 |0, 2, 2, 4, 6, 6, 7, 8, 8 |

|7 |0, 0, 1, 3, 4, 5, 5, 7 |

|8 |1, 2, 2 |

Key: 4 | 7 represents 47 sweets

(a) For the pupils’ estimates, write down

(i) the median;

(ii) the lower quartile;

(iii) the upper quartile.

(3)

(b) Draw a box and whisker plot of the pupils’ estimates using the grid below.

[pic]

(3)

(Total 6 marks)

4. 120 Mathematics students in a school sat an examination. Their scores (given as a percentage) were summarized on a cumulative frequency diagram. This diagram is given below.

[pic]

(a) Complete the grouped frequency table for the students.

|Examination |0 ≤ x ≤ 20 |20 < x ≤ 40 |40 < x ≤ 60 |60 < x ≤ 80 |80 < x ≤ 100 |

|Score x (%) | | | | | |

|Frequency |14 |26 | | | |

(3)

(b) Write down the mid-interval value of the 40 < x ≤ 60 interval.

(1)

(c) Calculate an estimate of the mean examination score of the students.

(2)

(Total 6 marks)

5. The cumulative frequency graph below shows the examination scores of 80 students.

[pic]

From the graph find

(a) the median value;

(b) the interquartile range;

(c) the 35th percentile;

(d) the percentage of students who scored 50 or above on this examination.

(Total 8 marks)

6. The cumulative frequency graph shows the amount of time in minutes, 200 students spend waiting for their train on a particular morning.

[pic]

(a) Write down the median waiting time.

(1)

(b) Find the interquartile range for the waiting time.

(2)

The minimum waiting time is zero and the maximum waiting time is 45 minutes.

(c) Draw a box and whisker plot on the grid below to represent this information.

[pic]

(3)

(Total 6 marks)

7. The diagram shows the cumulative frequency graph for the time t taken to perform a certain task by 2000 men.

[pic]

(a) Use the diagram to estimate

(i) the median time;

(ii) the upper quartile and the lower quartile;

(iii) the interquartile range.

(4)

(b) Find the number of men who take more than 11 seconds to perform the task.

(3)

(c) 55 % of the men took less than p seconds to perform the task. Find p.

(2)

The times taken for the 2000 men were grouped as shown in the table below.

|Time |Frequency |

|5 ≤ t < 10 |500 |

|10 ≤ t < 15 |850 |

|15 ≤ t < 20 |a |

|20 ≤ t < 25 |b |

(d) Write down the value of

(i) a;

(ii) b.

(2)

(e) Use your graphic display calculator to find an estimate of

(i) the mean time;

(ii) the standard deviation of the time.

(3)

Everyone who performs the task in less than one standard deviation below the mean will receive a bonus. Pedro takes 9.5 seconds to perform the task.

(f) Does Pedro receive the bonus? Justify your answer.

(3)

(Total 17 marks)

8. The bar chart below shows the number of people in a selection of families.

[pic]

(a) How many families are represented?

(b) Write down the mode of the distribution.

(c) Find, correct to the nearest whole number, the mean number of people in a family.

(Total 4 marks)

9. The table below shows the number of words in the extended essays of an IB class.

[pic]

(a) Draw a histogram on the grid below for the data in this table.

[pic]

(3)

(b) Write down the modal group.

(1)

The maximum word count is 4000 words.

(c) Write down the probability that a student chosen at random is on or over the word count.

(2)

(Total 6 marks)

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