Tutorial 2
Measures of central tendency: mean, median, mode.
Measure of Dispersion: range, variance and standard deviation.
N
Population mean,  
N
 xi
Population standard deviation,  
i 1
N
n
Sample mean, x 
x
i 1
 x
i 1
N
n
i
Sample standard deviation, s 
n
Coefficient of variation CV 
 x
i 1
 
2
i
 x
2
i
n 1
s
x
1) Which measures of central tendency can be used for both numerical and categorical
variables?
2) These are prices of six textbooks you have to buy for next semester:
RM25
RM7
RM22
RM63
RM18
RM15
Find the mean, median and mode for the price of the textbooks.
2) Distribution of 6 scores has a median of 21. If the highest score increases 3 points, the
median will become ___________.
3) Last year a small statistical consulting company paid each of its five statistical clerks
$22,000, two statistical analysts $50,000 each, and the senior statistician/owner $270,000.
The number of employees earning less than the mean salary is:
4) A sample of underweight babies was fed a special diet and the following weight gains (lbs)
were observed at the end of three month.
6.7
2.7
2.5
3.6
3.4
The mean and standard deviation are:
4.1
4.8
5.9
8.3
5) Rainwater was collected in water collectors at thirty different sites near an industrial basin
and the amount of acidity (pH level) was measured. The mean and standard deviation of
the values are 4.60 and 1.10 respectively. When the pH meter was recalibrated back at the
laboratory, it was found to be in error. The error can be corrected by adding 0.1 pH units to
all of the values and then multiply the result by 1.2. The mean and standard deviation of
the corrected pH measurements are:
6) Earthquake intensities are measured using a device called a seismograph which is designed
to be most sensitive for earthquakes with intensities between 4.0 and 9.0 on the open-ended
Richter scale. Measurements of nine earthquakes gave the following readings:
4.5
L
5.5
H
8.7
8.9
6.0
H
5.2
where L indicates that the earthquake had an intensity below 4.0 and H indicates that the
earthquake had an intensity above 9.0. The median earthquake intensity of the sample is:
7) If the mean of a numerical data set exceeds the median, the data are considered to be
____________ skewed.
8) The following data represent the price (in cents) of 100 grams of red chillies in the local
market for 20 consecutive days.
52
46
51
44
50
57
50
58
65
55
55
51
53
60
55
62
52
60
47
58
Compute
a) The mean, median and mode
b) The variance and standard deviation
c) The coefficient of variation
d) Using Excel get a summary statistics and histogram. Is the data skewed?
9) The time taken by 60 students to answer a probability question is recorded as given in the
table below.
Time (minutes)
Frequency (no. of students)
1
2
2
4
3
21
4
18
5
10
6
4
Find the mean, median and standard deviation of the time taken by the students in
answering the questions.
7
1
10) The following data is the burning times of chemical flares of two different formulations.
Type 1
Type 2
65
82
64
56
81
67
71
69
57
59
83
74
66
75
59
82
82
70
65
79
a) For each batch of data compute the mean, median and standard deviation.
b) Calculate the coefficient of variation and compare them. Which set of data is more
variable?