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Problem Solving and Data Analysis
14 – Median, Mean and Range
Calculator Required
The annual natural gas production of the Middle Eastern countries is recorded in the dot plot below.
Each value is rounded to the nearest 10 billion cubic meters.
According to the dot plot, how many Middle Eastern countries recorded an annual gas production of 30 billion
cubic meters or less?
13
According to the dot plot, what is the median annual natural gas production, in billions of cubic meters?
10
According to the dot plot, what is the mean annual natural gas production, in billions of cubic meters?
30.56
According to the dot plot, what is the range of annual natural gas production, in billions of cubic meters?
160
Students at schools in different states calculated the volume of snow that it took to
fill one cup of water after the snow had melted. Their results, in cups, were:
3.7, 3.0, 3.9, 2.5, 2.5, 2.2
To the nearest tenth of a cup, how much greater was the mean than the median of
their calculations?
Mean = 2.967
Median = 2.75
Difference = 0.2
Elena mailed 6 packages, with the following shipping charges.
$6.15, $4.78, $5.61, $4.41, $4.21, $6.54
If she mails a 7th package for $5.61, how will that affect the median shipping
charge?
A. The median will remain the same.
Current Median: 5.195
New Median: 5.61
B. The median will increase by $0.05.
C. The median will increase by $0.41.
D. The median will increase by $0.60.
An AP teacher recorded the scores on last year’s AP exams in the frequency table below.
Score
Count
5
7
4
11
3
7
2
2
1
2
According to the frequency table, how many students took the AP exam?
29
According to the frequency table, what is the median score on the AP exam? Hint: It might help to list the
scores.
1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5
4
According to the frequency table, what is the mean score on the AP exam? Round to the nearest hundredth if
necessary.
3.66
A local hardware store keeps track of the amount of money each customer spends during the first
week of June. The store rounded the totals to the nearest $10 and recorded their data in the
frequency table below.
Amount
$70
$60
$50
$40
$30
$20
$10
Frequency
43
49
37
33
83
66
22 22 – Not enough
171 – Found
88 – Not enough
According to the frequency table, how many customers shopped at the hardware store this week?
333
According to the frequency table, what is the median amount of money spent at the store?
There are too many values to list out.
Since there are 333 values, the median will be the 167th value.
(166 less than the median, the median, 166 greater than the median).
Starting from the smallest amount, find where the 167th value would fall.
30
According to the frequency table, what is the mean amount of money spent at the store?
70 * 43  60 * 49  50 * 37  40 * 33  30 * 83  20 * 66  10 * 22
 $39.49
333
The annual natural gas production of the Middle Eastern countries is recorded in the dot plot below.
Each value is rounded to the nearest 10 billion cubic meters.
If the country with the highest annual natural gas production was removed from the dot plot, how would the
median change?
It would not change; it would remain 10.
If the country with the highest annual natural gas production was removed from the dot plot, how would the
mean change?
It would decrease. The new mean would be 22.94.
Adding or removing extremely large or extremely small values typically affects the mean more than the median.
If an extreme value is added, the mean shifts towards the new value. (Adding a large value increases the mean.)
If an extreme value is removed, the mean shifts away from the removed value. (Removing a large value decreases the mean.)
The dot plot below depicts the daily high temperatures in degrees Fahrenheit during the first week of
April, 2014 in Anchorage, Alaska.
According the to dot plot above, what is the median daily high temperature for the first week of April?
41
According the to dot plot above, what is the mean daily high temperature for the first week of April?
41.14
According the to dot plot above, what is the range of daily high temperatures for the first week of April?
16
What would happen to the median if the lowest temperature, 31 degrees Fahrenheit, was replaced
with a new lowest temperature of 40 degrees Fahrenheit?
A. It would increase
B. It would decrease
C. It would stay the same
D. Not enough information
What would happen to the mean if the lowest temperature, 31 degrees Fahrenheit, was replaced with
a new lowest temperature of 40 degrees Fahrenheit?
A. It would increase
B. It would decrease
C. It would stay the same
D. Not enough information