COMPARING MEAN AND MEDIAN WORKSHEET
About "Comparing mean and median worksheet"
Comparing mean and median worksheet :
Worksheet on comparing mean and median is much useful to the students who would like to practice solving problems on measures of center.
Comparing mean and median worksheet - Problems
Problem 1 :
The monthly earnings of several teenagers are $200, $320, $275, $250, $750, $350, and $310.
Questions :
(i) Find the mean. Round to the nearest tenth.
(ii) Write the data values in order from least to greatest and find the median.
(iii) What is the difference between the mean and the median ? Why ?
(iv) Which measure of center better describes the typical monthly earnings for this group of teenagers—the mean or the median ? Explain.
Problem 2 :
Luka’s final exam scores for this semester are 70, 72, 99, 72, and 69.
Questions :
(i) Find the mean.
(ii) Write the data values in order from least to greatest and find the median.
(iii) What is the difference between the mean and the median ? Why ?
(iv) Which is a better description of Luka’s typical exam score ? Explain your thinking.
Comparing mean and median worksheet - Solution
Problem 1 :
The monthly earnings of several teenagers are $200, $320, $275, $250, $750, $350, and $310.
Questions (i) :
Find the mean. Round to the nearest tenth.
Answer :
Mean = (200 + 320 + 275 + 250 + 750 + 350 + 310) / 7
Mean = 2455 / 7
Mean = 350.7142........
Rounding to the nearest tenth
Mean = 350.7
Questions (ii) :
Write the data values in order from least to greatest and find the median.
Answer :
200, 250, 275, 310, 320, 350, 750
Number of observations (n) = 7
Median = [(n+1)/2] th value
Plug n = 7
Median = [(7+1)/2] th value
Median = 4 th value
Median = 310
Questions (iii) :
What is the difference between the mean and the median ? Why ?
Answer :
Difference between mean and median = |350.7 - 310|
Difference between mean and median = 40.7
Reason :
The mean is affected by the data value 750, which is much greater than the other data values. The median is not affected by this value.
Questions (iv) :
Which measure of center better describes the typical monthly earnings for this group of teenagers—the mean or the median? Explain.
Answer :
Median; The mean is greater than all but one of the data values. The median is a more central value.
Problem 2 :
Luka’s final exam scores for this semester are 70, 72, 99, 72, and 69.
Questions (i) :
Find the mean.
Answer :
Mean = (70 + 72 + 99 + 72 + 69) / 5
Mean = 382 / 5
Mean = 76.4
Questions (ii) :
Write the data values in order from least to greatest and find the median.
Answer :
69, 70, 72, 72, 99
Number of observations (n) = 5
Median = [(n+1)/2] th value
Plug n = 5
Median = [(5+1)/2] th value
Median = 3 rd value
Median = 72
Questions (iii) :
What is the difference between the mean and the median ? Why ?
Answer :
Difference between mean and median = |76.4 - 72|
Difference between mean and median = 4.4
Reason :
The mean is affected by the data value 99, which is much greater than the other data values. The median is not affected by this value.
Questions (iv) :
Which is a better description of Luka’s typical exam score? Explain your thinking.
Answer :
Median; the median is closer in value to most of the data values than the mean.
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