Stat 101 – Sheet 3
King Saud University
Almajmaa’h Engineering College
STAT 101
1430/2009
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Sheet (3)
1. The following data give the numbers of car thefts that occurred in a city
during the past 12 days:
6
3
7
11
4
3
8
7
2
6
9
15
Find the mean, median, and mode.
2. The mean age of six persons is 46 years. The ages of five of these six
persons are 57, 39, 44, 51, and 37 years. Find the age of the sixth person.
3. The mean 2004 income for five families was $69,520. What was the total
income of these five families?
4. Consider the following two data sets:
Data set I:
12
25
37
8
41
Data set II: 19
32
44
15
48
Notice that each value of the second data set is obtained by adding 7 to the
corresponding value of the first data set. Calculate the mean of these two
data sets. Comment on the relationship between the two means.
5. Consider the following two data sets:
Data set I:
4
Data set II: 8
Dr. SaMeH
8
15
9
11
16
30
18
22
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Stat 101 – Sheet 3
Notice that each value of the second data set is obtained by multiplying the
corresponding value of the first data set by 2. Calculate the mean of these
two data sets. Comment on the relationship between the two means.
6. The trimmed mean is calculated by dropping a certain percentage of values
from each end of a ranked data set. The trimmed mean is a especially
useful as a measure of central tendency when a data set contains a few
outliers at each end. Suppose the following data give the age of 10
employees of a company:
47
53
38
26
39
49
19
67
31
23
To calculate the 10% trimmed mean, first rank these data values in
increasing order; then drop 10% of the smallest values and 10% of the
largest value. The mean of the remaining 80% of the values will give the
10% trimmed mean. This data set contains 10 values, and 10% is 1. Hence,
drop the smallest value and the largest value from this data set. The mean
of the remaining 8 values will be the 10% trimmed mean. Calculate the 10%
trimmed mean for this data set.
7. If we know the means and sample sizes of two (or more) data sets, we can
calculate the combined mean of both (or all) data sets.
̅=
𝒄𝒐𝒎𝒃𝒊𝒏𝒆𝒅 𝒎𝒆𝒂𝒏 = 𝒙
̅ 𝟏 + 𝒏𝟐 ̅
𝒏𝟏 𝒙
𝒙𝟐
𝒏𝟏 + 𝒏𝟐
Where n1 and n2 are the sample sizes of the two data sets and 𝑥̅1 and 𝑥̅2 are
the means of the two data sets respectively. Suppose a sample of 10
statistics books gave a mean price of $95 and a sample of 8 mathematics
books gave a mean price of $104. Find the combined mean.
8. Explain the relationships among the mean, median, and mode for
symmetric and skewed histograms. Illustrate these relationships with
graphs.
Dr. SaMeH
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