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20 Jun 2021, 17:42
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B
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Difficulty:
15%
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Question Stats:
83% (01:08) correct
17%
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wrong
based on 107
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The following represents the verbal scores of 30 test-takers in a popular test.
166 166 167 168 168 169 169 169 169 170
170 170 170 170 170 170 170 170 170 170
170 170 170 170 170 170 170 170 170 170
What is the relationship among the mean, median and mode?
A. Median < Mean < Mode
B. Mean < Median = Mode
C. Median < Mean = Mode
D. Mean< Median< Mode
E. Median =Mean < Mode
166 166 167 168 168 169 169 169 169 170
170 170 170 170 170 170 170 170 170 170
170 170 170 170 170 170 170 170 170 170
What is the relationship among the mean, median and mode?
A. Median < Mean < Mode
B. Mean < Median = Mode
C. Median < Mean = Mode
D. Mean< Median< Mode
E. Median =Mean < Mode
21 Jun 2021, 04:22
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The mode is the most 'popular' value, and we have tons of 170s, so that's the mode. The median is the middle value when you list things in increasing order, as the table does, and we can see our median will be somewhere in the middle of the second row, so it's certainly also 170. The table has a lot of 170s, which average out to 170, but when we then add in the few values below 170, those will drag the average down a bit, so the mean is slightly less than 170. So mean < median = mode.
31 Jul 2022, 23:24
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Theory
In the given set of 30 values
166 166 167 168 168 169 169 169 169 170
170 170 170 170 170 170 170 170 170 170
170 170 170 170 170 170 170 170 170 170
Most the values are 170 (21), Some are 169 (4), Some are 168 (2) and we have 167 and 166 (2 values)
Median of the set is the middle value = mean of Middle two values in this case as we have even number of values (30)
=> Mean of 170 and 170 = 170
Mode of the set is 170 as 170 has occurred the maximum number of times.
Mean of the set = Sum of all the values /30. Now most of the values are 170 and some values are less than 170. So Mean will also be less than 170.
=> Mean (<170) < Median (170) = Mode (170)
So, Answer will be B.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
- ➡ Mean is the average of the all the numbers in the set.
➡ Median is the middle value of the set.
➡ Mode is the number which has occurred the maximum number of times in the set.
In the given set of 30 values
166 166 167 168 168 169 169 169 169 170
170 170 170 170 170 170 170 170 170 170
170 170 170 170 170 170 170 170 170 170
Most the values are 170 (21), Some are 169 (4), Some are 168 (2) and we have 167 and 166 (2 values)
Median of the set is the middle value = mean of Middle two values in this case as we have even number of values (30)
=> Mean of 170 and 170 = 170
Mode of the set is 170 as 170 has occurred the maximum number of times.
Mean of the set = Sum of all the values /30. Now most of the values are 170 and some values are less than 170. So Mean will also be less than 170.
=> Mean (<170) < Median (170) = Mode (170)
So, Answer will be B.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
