Exam

Premium

Department

Statistics

Course Code

STAB22H3

Professor

All

Study Guide

Midterm

University of Toronto Scarborough

STAB22 Midterm Examination solutions

June 2007

This examination contains a mixture of short-answer and multiple choice questions. For

the short-answer questions, write your answers in the spaces provided; for the multiple-choice

questions, circle the best answer out of the alternatives given.

Marks for each question are as shown.

Correct answers for multiple-choice questions are shown by a *.

1

1. (5 marks) At a certain university in 1993, a record was kept of the number of women

graduating with doctoral degrees in each of six diﬀerent ﬁelds of study.

(a) What is this kind of graph usually called?

i. Histogram

ii. * Bar chart (the variable “ﬁeld of study” is categorical)

iii. Stem-and-leaf plot

iv. Pie chart

(b) Which ﬁeld of study had the most women graduating with doctoral degrees in

1993?

Psychology

(c) Approximately how many women graduated with doctoral degrees in life sciences

in 1993?

40 (or 39 if that’s what you think it is)

2. (8 marks) A political scientist takes a large sample of registered voters, and measures a

number of variables, as shown below. Are each of the variables listed below categorical

or quantitative?

(a) Gender

i. * Categorical

ii. Quantitative

(b) Age

i. Categorical

ii. * Quantitative

(c) Household income

i. Categorical

2

ii. * Quantitative

(d) Party voted for at last election

i. * Categorical

ii. Quantitative

3. (5 marks) What is the median of the following set of numbers: 7, 6, 10, 9, 5?

(a) 7.4

(b) * 7 (remember to arrange the numbers in order ﬁrst!)

(c) 10

(d) 6

4. (7 marks) The speeds of 57 cars were measured (in km/h) on a city street. A numerical

summary of the results is given below:

Descriptive Statistics: speed

Variable N N* Mean SE Mean StDev

speed 57 0 45.53 1.64 12.38

Variable Minimum Q1 Median Q3 Maximum

speed 25.60 36.80 43.20 51.20 83.20

Do a calculation to decide whether the highest recorded speed, 83.2 km/h, is an outlier

in this data set. What do you conclude?

IQR is 51.20−36.80 = 14.4; 1.5 ×IQR is 21.6; Q3 plus this is 51.2+21.6 =

72.8. The maximum value is 83.2, bigger than this, so is an outlier by this

criterion.

5. (3 marks) A delivery company recorded the delivery costs for 39 small packages it

delivered one day last week. A histogram of the delivery costs is shown below.

3

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