Classifying Data, Averages and Range — Solutions
Full worked solutions, with method and final answer for every part.
Question 1
(a)Mean = sum of values ÷ number of values = 57 ÷ 7.
≈ 8.14 (3 s.f.)
Question 2
(a)The data is already in order; the middle value (4th of 7) is the median. The most frequent value is the mode.
Median = 8, mode = 7
Question 3
(a)Range = highest value − lowest value.
12 − 4 = 8
Question 4
(a)Mean = sum ÷ count = 157 ÷ 8.
≈ 19.6 (3 s.f.)
Question 5
(a)With 8 values (even count), the median is the mean of the 4th and 5th values (18 and 20).
(18+20)/2 = 19
Question 6
(a)Mode is the most frequent value (15 appears twice); range = highest − lowest.
Mode = 15, range = 30 − 12 = 18
Question 7
(a)The mean is pulled strongly toward an extreme outlier, since every value affects its total, whereas the median depends only on the middle value(s) and is barely affected by one extreme value.
The median is not distorted by an extreme outlier the way the mean is
Question 8
(a)Mean = sum ÷ count = 41 ÷ 8.
≈ 5.13 (3 s.f.)
Question 9
(a)If no value repeats, or several values are tied for most frequent, the mode gives little useful information about the data's centre — e.g. a data set with all different values has no mode at all.
The mode can be undefined or unhelpful when no value clearly repeats more than others
Question 10
(a)Adding a value (50) that is higher than the current mean (20) pulls the mean upward.
The new mean will be higher than 20
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