Reflection 8: STATISTICS

G. Tawfik

A. ANALYSIS

P. 273 # 2 b,d,g

1. In each of the following cases, state whether it is better to make a census, poll or survey:

a. the annual inventory is made of merchandise in a store specializing in electronics.

b. a radio station wants to find out the average age and income of its listeners.

c. A pharmaceutical company wants to find out what side effects are linked to the absorption
of a new medication it plans to manufacture.

P. 279 #1 c,d,e

2. In each of the following cases, state whether the sample formed is representative of the
target population. Justify your answer.

a.    the owner of a junior hockey team is concerned about the drop in attendance at games.
        At a local game, he asks 40 supporters, chosen at random, to explain what they thought
        was behind this poor attendance.

b.    An election organizer wants to predict the voting intentions of Quebeckers for the
        upcoming elections. She requests that a poll be taken among 1000 residents of Montreal
        and 500 residents of Quebec City.

c.    A car dealer wants to determine the degree of satisfaction of his clients. He phones
        80 people, selected at random, from among those clients who bought a car from him
        in the past 7 years.

P. 296 # 3

3.    Anne-Marie wants to find out the average weekly income of the 16-year-olds who are part of
        18 class-groups in three high schools of her school board. She phones 25 of her friends and
        calculates the average weekly income of those who agreed to respond.

a. Why is this sample not representative? Give three reasons.

b. Describe a sampling method Anne-Marie could have used to obtain a representative sample.

B. QUARTILES: Stem-and-Leaf and Box-and-whiskers

P. 297, P. 304 # 7, 9

1. Twenty-five teenagers are playing bowling. Their scores are shown below:

123 99 139 100 88 86 133 100 153 112 93 107 73 131 169 95 105 111 91 138 77 80 102 116 128

a.    Construct the stem-and-leaf plot for the given scores.
b.    What are the worst and best scores?
c.    Which score is located exactly in the middle of the given scores? This is the median
d.    Determine the median of the set of scores less than the median in (c). This is Q₁.
e.    Determine the median Q₃ of the set of scores greater than the median in (c).
f.    How many data are:
            i. less than Q₁?
            ii. between Q₁ and Q₂?
            iii. between Q₂ and Q₃?
            iv. greater than Q₃?
g.    Construct the box-and-whiskers plot for these data.

2. Radar is used to monitor the speed of a cars travelling on a highway.
The stem-and-leaf plot below gives these data.

a.    The speed limit is 100 km/h. What percent of drivers respected the speed limit?
b.    Construct a box-and-whiskers plot to represent these data.
c.    If the median is 109, in which quarter is the other 109 located?
d.    By studying the plot determine if it is possible to state that:

i. half the drivers exceeded the speed limit by more than 10 km/h.
ii. The data are mostly grouped around the median.

3. A nurse weighed the 200 third-grade students in a school.
The following box-and-whisker plot presents her results:

a. Determine the numerical data revealed by the plot: minimum,
quartiles, maximum, range and interquartile range.
b. Is it true that 100 students weigh 30 kg or more?
c. Give at least two other conclusions based on the data in this graph.

C. QUINTILES

P. 310 # 2, 4

1. A test was drawn up to select the students who will represent the school at the Opti-Math contest.
The results of the test are given below:

122 124 126 127 133 138 139 142 144 150 153 156 157 163 166 170 173 175 178 179 180 185 190

a. Only the results found in quintile rank 1 will be kept. Give these results.

b. Give the quintile rank of the mark 145.

c. Give the quintile rank of the median.

2. The results of the last two exams in the term for the students in Isabelle's class are given:

Test 1:

12 14 15 16 18 20 21 22 23 24 24 24 25 25
27 27 28 30 30 32 32 34 35 37 38 38 39 40 40

Test 2:

30 32 32 33 34 36 37 38 40 42 42 42 44 45 45
46 47 47 48 50 52 52 54 55 57 58 60 (1 absentee)

Both of Isabelle's results are underlined.
In comparison to her group, on which test are her results better?

D. PERCENTILES

P. 322 #1

Given the following distribution:

12 14 17 19 24 27 32 34 34 48 40 44 46 49 54 65 72 74 84

a. Which value has the following percentile rank?
i. 20 ii. 25 iii. 40 iv. 90

b. What is the percentile rank of each of the following values?
i. 84 ii. 49 iii. 34 iv. 27

POPQUIZ

1. A class of 30 students obtained the following percentage marks on their last Math test.

70, 70, 71, 72, 73, 74, 75, 76, 76, 77, 77, 78, 79, 80, 80,

81, 81, 86, 86, 87, 87, 88, 90, 90, 92, 93, 94, 95, 95, 96

a. Which marks correspond to the 5th quintile rank?
b. Which quintile rank is assigned to a mark of 86?

c. Construct the box-and-whisker plot for this distribution.

d. Between which quartiles are the data most concentrated?

2. Of the 70 participants in a women's downhill skiing competition, Jackie finished 8th and Maxime
finished 10th .

a. What is Jackie's percentile rank?

b. What is Maxime's percentile rank?

c. In which place did Laura finish if she got a percentile rank of 40?

3. A Secondary IV class obtained the following percentage marks on their English exam:

42, 63, 79, 93, 85, 80, 72, 60, 72, 49, 53, 69, 78. 88, 73,

82, 60, 68, 73, 81, 88, 94, 79, 86, 80, 89, 68, 74, 62

a. What is the range of these marks?
b. Determine the interquartile range.

c. Make an observation concerning the concentration of data in this distribution.

R8 Answers to PopQuiz

1. a. 110, 110, 111, 112, 113, 114

b. R5 (126) = 2

d. [Q1, Med]

2. a. R100 (Jackie) = 90

b. R100 (Maxime) = 88

c. Rank (40) = 43rd

3. a. Range = Max - Min = 94 - 42 = 52

b. IQR = Q3 - Q1 = 83,5 - 65,5 = 18

c. Data dispersed in [Min, Q1] Equal concentration in other quarters.