# Exercises Tutorial 2

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```					                    Exercises Tutorial 2
ec1030, Stats

Jacco Thijssen

1. Find news stories from this week in which measures of central tendency,
variability, and association play a role.

2. A sociologist randomly sampled 10 areas in Ireland and recorded the
percentage of households per area involved in a particular government
program. The results were: 10.2, 2.9, 3.1, 6.8, 5.9, 7.3, 7.0, 8.2, 3.7, 4.3.

(a) Calculate the mean percentage of households involved in the pro-
gram.
(b) Calculate the median.
(c) Comment on the shape of the distribution (symmetry).

3. The time (in minutes) that it took a random sample of students to per-
form a test is

23   35   14       37   28   45
12   40   27       13   26   25
37   20   29       49   40   13
27   16   40       20   13   66

(a) Find the mean time.
(b) Find the standard deviation.
(c) Find the ﬁve-number summary.
(d) Find the coeﬃcient of variation.

4. Use Chebyshev’s rule to approximate each of the following observations
if the mean is 250 with a standard deviation of 20. Approximately what
proportion of the observations is

1
(a) between 190 and 310?
(b) between 210 and 290?
(c) between 230 and 270?

5. A lecturer in statistics is interested in the link between tutorial atten-
dance and exam score. For one term he considered a random sample of
students and recorded the number of seminars (out of 9) that they had
visited and their score in an end-of-term test (out of 100). The data are
given below.1

(5,53)   (6,56)    (6,48)       (6,65)   (4,35)   (2,45)
(7,63)   (8,78)    (7,76)       (7,42)   (3,89)   (3,25)
(9,24)   (1,23)    (5,46)       (8,57)   (9,65)   (4,13)
(2,90)    (0,2)    (4,67)       (7,10)   (9,45)   (7,66)

(a) Compute the covariance.
(b) Compute the correlation coeﬃcient.
(c) Brieﬂy discuss the relationship between tutorial attendance and
end-of-term test performance.

6. Four each of the samples below (with identical means), arrange the sam-
ples according to the magnitudes of their standard deviation, without
doing any computation. Then calculate each of the variances.

• 1,2,3,4,5,6,7,8
• 1,1,1,1,8,8,8,8
• 1,1,4,4,5,5,8,8
• -6,-3,0,3,6,9,12,15

7. There appears to be a perception that2 that the percentage of degrees
awarded in the second upper and ﬁrst classes (II.1 and I) has increased
substantially. Especially in the UK, employers are therefore claiming
1
The data are ﬁctional. For next year’s tutorial I will use a random sample obtained
from this year’s cohort (i.e. you).
2
I have not looked at any data and – therefore – make this statement with caution.

2
there should yet be another degree class (usually referred to as II.1∗). Us-
ing the concepts of “central tendency” and “variability”, describe reasons
why employers would want this. From a student’s perspective, would you
be in favour of an additional degree class?

3

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