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Worksheet 1 - Chapter (1): Introduction to Statistics – Solutions
Q–1: The mode of the data 23, 27, 23, 25, 32, 30, 23, 25, 26 is
a) 32
(b) 23
(c) 26
(d) 25
(e) None of the above
Q–2: The median of the sample data 1, 3, 5, 6, 8, 9, 11, 16 is
a) 6
(b) 7
(c) 8
(d) 16
(e) None of the above
Q–3: The sample mean of the data 23, 27, 23, 25, 32, 30, 23, 25, 26 is
a) 32
(b) 26
(c) 25
(d) 23
(e) None of the above
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Q–4: The following measurements were recorded for the drying time, in hours, of a certain brand of
latex paint:
3.1, 2.6, 2.9, 3.2, 2.8, 3.3, 3.5, 3.0
a) Calculate the sample mean.
x
2.6  2.8  2.9  3.0  3.1  3.2  3.3  3.5
 3.05
8
b) Calculate the sample median.
2.6, 2.8, 2.9, 3.0, 3.1, 3.2, 3.3, 3.5
3.0  3.1
~
x
 3.05
2
c) Find the sample range.
range  max  min  3.5  2.6  0.9
d) Calculate the sample variance and standard deviation.
(𝑥𝑖 − 𝑥̅ )
2.6 -3.05 = -0.45
2.8 – 3.05 =-0.25
2.9 – 3.05 =-0.15
3.0 – 3.05 =-0.05
3.1 – 3.05 =0.05
3.2 – 3.05 = 0.15
3.3 – 3.05 = 0.25
3.5 – 3.05 = 0.45
∑(𝑥𝑖 − 𝑥̅ )2
 (x

 x)2
(𝑥𝑖 − 𝑥̅ )2
0.2025
0.0625
0.0225
0.0025
0.0025
0.0225
0.0625
0.2025
0.58
0.58
 0.085
n 1
8 1
S tan dardDeviation  S  0.085  0.288
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Variance  S
2
i

Q–5: A list of temperatures of 9 days in November taken from the meteorological records of an Arab
city is
25, 32, 23, 30, 27, 23, 26, 25, 23.
a) Calculate the sample mean for these data.
x
23  23  23  25  25  26  27  30  32
 26
9
b) Calculate the mode.
23, 23, 23, 25, 25, 26, 27, 30, 32
mode  23
c) Find the sample range.
range  max - min  32 - 23  9
d) Calculate the sample variance and standard deviation.
s 2  10.25 & s  3.2
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Q−6: A tire manufacturer wants to determine the inner diameter of a certain grade of tire. Ideally, the
diameter would be 570 mm. The data are as follows:
572, 572, 573, 568, 569, 575, 565, 570.
a) Find the sample mean. X  570.5.
~
b) Find the sample median. X  571.
c) Find the sample range. Range  max  min  575  565  10.
d) Find the sample variance and standard deviation.
S 2  10, S  3.162 .
e) Using the calculated statistics can you comment on the quality of the tires?
Variance of the diameters seems too big so the manufacturing quality is questionable.
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Q−7: The following are historical data on staff salaries (dollars per pupil) for 30 schools sampled in the
eastern part of the United States in the early 1970s.
3.79, 2.99, 2.77, 2.91, 3.10, 1.84, 2.52, 3.22, 2.45, 2.14, 2.67,
2.52, 2.71, 2.75, 3.57, 3.85, 3.36, 2.05, 2.89, 2.83, 3.13,
2.44, 2.10, 3.71, 3.14, 3.54, 2.37, 2.68, 3.51, 3.3
a) Compute the sample mean and sample standard deviation.
X  2.8973, S  0.5415
b) Use the data to construct a box plot.
Min:
1.84
Max:
3.58
Median: Q2
2.86
Lower quartile: Q1 2.52
Upper quartile: Q3 3.30