Author: Chase Brooks
Company: Hall County Board of Education

Name: _________________________________ Date: _____________ Period: __________

Topic 2 - Statistics Test Review
94 marks
1.	The mean of the ten numbers listed below is 5.5.
4, 3, a, 8, 7, 3, 9, 5, 8, 3
(a)	Find the value of a.
(b)	Find the median of these numbers.
Working: |

Answers:
(a)	…………………………………………..
(b)	…………………………………………..

(Total 4 marks)

2.	The table shows the number of children in 50 families.

Number of
children

Frequency

Cumulative
frequency

1 | 3 | 3
2 | m | 22
3 | 12 | 34
4 | p | q
5 | 5 | 48
6 | 2 | 50
| T |

(a)	Write down the value of T.
(b)	Find the values of m, p and q.
Working: |

Answers:
(a)	…………………………………………..
(b)	…………………………………………..

(Total 4 marks)
3.	Twenty students are asked how many detentions they received during the previous week at school. The results are summarised in the frequency distribution table below.

Number of
detentions
x

Number of
students
f

fx

0 | 6 |
1 | 3 |
2 | 10 |
3 | 1 |
Total | 20 |
 
(a)	What is the modal number of detentions received?
 
(b)	(i)	Complete the table.
(ii)	Find the mean number of detentions received.

Working: |

Answers:
(a)	..................................................................
(b)	(ii)	……………………………………...

(Total 4 marks)

 4.	The weight in kilograms of 12 students in a class are as follows.
	63  76  99  65  63  51  52  95  63  71  65  83
(a)	State the mode.
(1)
 
(b)	Calculate
(i)	the mean weight;
(ii)	the standard deviation of the weights.
(2)
 
	When one student leaves the class, the mean weight of the remaining 11 students becomes 70 kg.
(c) Find the weight of the student who left.
(2)
(Total 5 marks)

5.	The table below shows the percentage, to the nearest whole number, scored by candidates in an examination.
Marks (%) | 0–9 | 10–19 | 20–29 | 30–39 | 40–49 | 50–59 | 60–69 | 70–79 | 80–89 | 90–100
Frequency | 2 | 7 | 8 | 13 | 24 | 30 | 6 | 5 | 3 | 2
	The following is the cumulative frequency table for the marks.
Marks (%) | Cumulative frequency
<   9.5 | 2
<  19.5 | 9
<  29.5 | s
<  39.5 | 30
<  49.5 | 54
<  59.5 | 84
<  69.5 | t
<  79.5 | 95
<  89.5 | 98
< 100 | 100
(a)	Calculate the values of s and of t.
(2)

(b)	Using a scale of 1 cm to represent 10 marks on the horizontal axis, and 1 cm to represent 10 candidates on the vertical axis, draw a cumulative frequency graph. You will need graph paper for question.
(3)

(c)	Use your graph to estimate
(i)	the median mark;
(ii)	the lower quartile;
(iii)	the pass mark, if 40% of the candidates passed.
(4)
(Total 9 marks)
6.	The following table shows the age distribution of teachers who smoke at Laughlin High School.
Ages | Number of smokers
20 ≤ x < 30 | 5
30 ≤ x < 40 | 4
40 ≤ x < 50 | 3
50 ≤ x < 60 | 2
60 ≤ x < 70 | 3
(a)	Calculate an estimate of the mean smoking age.

(b)	On the following grid, construct a histogram to represent this data.

Working: |

Answers:
(a)	…………………………………………..

(Total 4 marks)
7.	The graph below shows the cumulative frequency for the yearly incomes of 200 people.

Use the graph to estimate
(a)	the number of people who earn less than 5000 British pounds per year;
(b)	the median salary of the group of 200 people;
(c)	the lowest income of the richest 20% of this group.
Working: |

Answers:
(a)	..................................................................
(b)	..................................................................
(c)	..................................................................

(Total 4 marks)

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

(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.
Working: |

Answers:
(a)	..................................................................
(b)	..................................................................
(c)	..................................................................

(Total 4 marks)

9.	The following stem and leaf diagram gives the heights in cm of 39 schoolchildren.
Stem | Leaf | Key   13 | 2   represents 132 cm.

13
14
15
16
17
18

2, 3, 3, 5, 8, 
1, 1, 1, 4, 5, 5, 9, 
3, 4, 4, 6, 6, 7, 7, 7, 8, 9, 9,
1, 2, 2, 5, 6, 6, 7, 8, 8,
4, 4, 4, 5, 6, 6,
0,

(a)	(i)	State the lower quartile height.
(ii)	State the median height.
(iii)	State the upper quartile height.

(b)	Draw a box-and-whisker plot of the data using the axis below.

(Total 6 marks)
10.	The speed of sound in air is given as 300 ms^–l.
(a)	How many metres does sound travel in air in one hour?
(b)	Express your answer to part (a)
(i)	correct to two significant figures;
(ii)	in the form a × 10^k, where 1 ≤ a < 10 and k Î .
Working: |

Answers:
(a)	..................................................................
(b)	(i)	...........................................................
	(ii)	...........................................................

(Total 4 marks)

11.	The sixth term of an arithmetic sequence is 24. The common difference is 8.
(a)	Calculate the first term of the sequence.

The sum of the first n terms is 600.
(b)	Calculate the value of n.
Working: |

Answers:
(a)	..................................................................
(b)	..................................................................

(Total 8 marks)

12.	Annie is starting her first job. She will earn a salary of $26000 in the first year and her salary will increase by 3% every year.
(a)	Calculate how much Annie will earn in her 5^th year of work.
(3)
Annie spends $24800 of her earnings in her first year of work. For the next few years, inflation will cause Annie’s living expenses to rise by 5% per year.
(b)	(i)	Calculate the number of years it will be before Annie is spending more than she earns.
(ii)	By how much will Annie’s spending be greater than her earnings
in that year?
(6)
(Total 9 marks)

13.	Members of a certain club are required to register for one of three games, billiards, snooker or darts.
	The number of club members of each gender choosing each game in a particular year is shown in the table below. 
| Billiards | Snooker | Darts
Male | 39 | 16 | 8
Female | 21 | 14 | 17
(a)	Use a (Chi-squared) test at the 5% significance level to test whether choice of games is independent of gender. State clearly the null and alternative hypotheses tested, the expected values, and the number of degrees of freedom used.
(13)
 
	The following year the choice of games was widened and the figures for that year are as follows:
| Billiards | Snooker | Darts | Fencing
Male | 4 | 15 | 8 | 10
Female | 10 | 21 | 17 | 37
(b)	If the  test were applied to this new set of data,
(i)	why would it be necessary to combine billiards with another game?
(ii)	which other game would you combine with billiards and why?
(2)
 
	A club member is to be selected at random.
(c)	What is the probability that the club member selected is a
(i)	female who chose billiards or snooker?
(ii)	male or female who chose darts or fencing?
(2)
(Total 17 marks)

14.	The Type Fast secretarial training agency has a new computer software spreadsheet package. The agency investigates the number of hours it takes people of varying ages to reach a level of proficiency using this package. Fifteen individuals are tested and the results are summarised in the table below.
Age | 32 | 40 | 21 | 45 | 24 | 19 | 17 | 21 | 27 | 54 | 33 | 37 | 23 | 45 | 18
(x) | | | | | | | | | | | | | | |
Time | | | | | | | | | | | | | | |
(in hours) | 10 | 12 | 8 | 15 | 7 | 8 | 6 | 9 | 11 | 16 | t | 13 | 9 | 17 | 5
(y) | | | | | | | | | | | | | | |
(a)	(i)	Given that S_y = 3.5 and S_xy = 36.7, calculate the product-moment correlation coefficient r for this data.
(4)
(ii)	What does the value of the correlation coefficient suggest about the relationship between the two variables?
(1)
 
(b)	Given that the mean time taken was 10.6 hours, write the equation of the regression line for y on x in the form y = ax + b.
(3)
 
(c)	Use your equation for the regression line to predict
(i)	the time that it would take a 33 year old person to reach proficiency, giving your answer correct to the nearest hour;
(2)
(ii)	the age of a person who would take 8 hours to reach proficiency, giving your answer correct to the nearest year.
(2)
(Total 12 marks)