Statistics - Mode, Range, Mean and Median
Question 1
Find the mode, range, mean and median for the following data sets:
a) $2,3,3,4,8$
a
Mode is $3$
Range is $6$
Mean is $4$
Median is $3$
Question ID: 70040010010
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b) $5,5,6,6,6,7,7$
a
Mode is $6$
Range is $2$
Mean is $6$
Median is $6$
Question ID: 70040010020
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c) $8,12,12,12,13,13,13,13$
a
Mode is $13$
Range is $5$
Mean is $12$
Median is $12.5$
Question ID: 70040010030
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d) $2,8,1,3,8,4,20,6$
a
Mode is $8$
Range is $19$
Mean is $6.5$
Median is $5$
Question ID: 70040010040
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e) $22,35,9,37,18,30,37,20$
a
Mode is $37$
Range is $28$
Mean is $26$
Median is $26$
Question ID: 70040010050
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f) $54,88,91,37,23,54,23,88,91,91$
a
Mode is $91$
Range is $68$
Mean is $64$
Median is $71$
Question ID: 70040010060
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g) $4.2,8.8,0.2,9.2$
a
There is no Mode
Range is $8.6$
Mean is $5.6$
Median is $6.5$
Question ID: 70040010070
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h) $0.5,0.6,0.5,0.4,0.5,0.5$
a
Mode is $0.5$
Range is $0.2$
Mean is $0.5$
Median is $0.5$
Question ID: 70040010080
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i) $184,102,98,98,137,156,98,184$
a
Mode is both $98$ and $184$
Range is $86$
Mean is $137$
Median is $137$
Question ID: 70040010090
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j) $44.8,25.7,100,0.1,56.5,100,0.8,0.1,25.7,56.5,100$
a
Mode is $100$
Range is $99.9$
Mean is $46\frac{21}{55}$
Median is $44.8$
Question ID: 70040010100
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Question 2
Compare the following data sets using the mode, range, mean and median:
a) Data set A: $4,5,7,9,10$
Data set B: $2,6,6,8,13$
a
Data set A:
No mode
Range is $6$
Mean is $7$
Median is $7$
Data set B:
Mode is $6$
Range is $11$
Mean is $7$
Median is $6$
Data set B is more varied according to the range, however their average ability is the same as they have the same range.
Question ID: 70040020010
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b) Data set A: $18,16,43,18,13,12$
Data set B: $24,16,20,20,19,21$
a
Data set A:
Mode is $18$
Range is $31$
Mean is $20$
Median is $17$
Data set B:
Mode is $20$
Range is $8$
Mean is $20$
Median is $20$
Data set A is more varied according to the range, however their average ability is the same as they have the same range. $43$ in Data Set A seems like an outlier, as is a much higher result. It may be necessary to retest this result. If it wasn't for $43$ Data Set B would have an overall higher average with a higher median.
Question ID: 70040020020
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c) Data set A: $19,4,1,25,1$
Data set B: $20,25,1,1,43$
a
Data set A:
Mode is $1$
Range is $24$
Mean is $10$
Median is $4$
Data set B:
Mode is $1$
Range is $20$
Mean is $45$
Median is $20$
. Data set B has a much higher mean, which is the more accurate measure here. The mode does not represent the data sets well, and the median is too large of a spread too.
Question ID: 70040020030
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Question 3
Answer the following worded questions
a) The range of the following data set is $11$ and the median is $8$. Find $x$ and $y$.
$x,5,y,8,14$
a
$x=3$, $y=8$
Question ID: 70040030010
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b) The median of the following data set is $22$ and the mean is $21$. Find $x$ and $y$.
$15,20,x,y,26$
a
$x=22$, $y=22$
Question ID: 70040030020
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c) The mode of the following data set is $5$, the range is 7 and the mean is $7$. Find $x$, $y$ and $z$.
$5,x,y,7,z$
a
$x=5$, $y=6$, $z=12$
Question ID: 70040030030
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d) Four numbers have a range of $6$, a mode of $4$ and a median of $5$. The largest number is $10$. Find the other three numbers.
a
$4,4$ and $6$
Question ID: 70040030040
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e) Four numbers have a range of $10$ and mode of $23$ and a median of $24$. Find the four numbers.
a
$23,23,25,33$
Question ID: 70040030050
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f) Five numbers have a mode of $46$, a median of $46$, a range of $24$ and a mean of $37$. Find the five numbers.
a
$23,24,46,46,46$
Question ID: 70040030060
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Question 1
Find the mode, range, mean and median for the following data sets:
a) $2,3,3,4,8$
b) $5,5,6,6,6,7,7$
c) $8,12,12,12,13,13,13,13$
d) $2,8,1,3,8,4,20,6$
e) $22,35,9,37,18,30,37,20$
f) $54,88,91,37,23,54,23,88,91,91$
g) $4.2,8.8,0.2,9.2$
h) $0.5,0.6,0.5,0.4,0.5,0.5$
i) $184,102,98,98,137,156,98,184$
j) $44.8,25.7,100,0.1,56.5,100,0.8,0.1,25.7,56.5,100$
Question 2
Compare the following data sets using the mode, range, mean and median:
a) Data set A: $4,5,7,9,10$
Data set B: $2,6,6,8,13$
b) Data set A: $18,16,43,18,13,12$
Data set B: $24,16,20,20,19,21$
c) Data set A: $19,4,1,25,1$
Data set B: $20,25,1,1,43$
Question 3
Answer the following worded questions
a) The range of the following data set is $11$ and the median is $8$. Find $x$ and $y$.
$x,5,y,8,14$
b) The median of the following data set is $22$ and the mean is $21$. Find $x$ and $y$.
$15,20,x,y,26$
c) The mode of the following data set is $5$, the range is 7 and the mean is $7$. Find $x$, $y$ and $z$.
$5,x,y,7,z$
d) Four numbers have a range of $6$, a mode of $4$ and a median of $5$. The largest number is $10$. Find the other three numbers.
e) Four numbers have a range of $10$ and mode of $23$ and a median of $24$. Find the four numbers.
f) Five numbers have a mode of $46$, a median of $46$, a range of $24$ and a mean of $37$. Find the five numbers.
Answers
Question 1
a) Mode is $3$
Range is $6$
Mean is $4$
Median is $3$
b) Mode is $6$
Range is $2$
Mean is $6$
Median is $6$
c) Mode is $13$
Range is $5$
Mean is $12$
Median is $12.5$
d) Mode is $8$
Range is $19$
Mean is $6.5$
Median is $5$
e) Mode is $37$
Range is $28$
Mean is $26$
Median is $26$
f) Mode is $91$
Range is $68$
Mean is $64$
Median is $71$
g) There is no Mode
Range is $8.6$
Mean is $5.6$
Median is $6.5$
h) Mode is $0.5$
Range is $0.2$
Mean is $0.5$
Median is $0.5$
i) Mode is both $98$ and $184$
Range is $86$
Mean is $137$
Median is $137$
j) Mode is $100$
Range is $99.9$
Mean is $46\frac{21}{55}$
Median is $44.8$
Question 2
a) Data set A:
No mode
Range is $6$
Mean is $7$
Median is $7$
Data set B:
Mode is $6$
Range is $11$
Mean is $7$
Median is $6$
Data set B is more varied according to the range, however their average ability is the same as they have the same range.
b) Data set A:
Mode is $18$
Range is $31$
Mean is $20$
Median is $17$
Data set B:
Mode is $20$
Range is $8$
Mean is $20$
Median is $20$
Data set A is more varied according to the range, however their average ability is the same as they have the same range. $43$ in Data Set A seems like an outlier, as is a much higher result. It may be necessary to retest this result. If it wasn't for $43$ Data Set B would have an overall higher average with a higher median.
c) Data set A:
Mode is $1$
Range is $24$
Mean is $10$
Median is $4$
Data set B:
Mode is $1$
Range is $20$
Mean is $45$
Median is $20$
. Data set B has a much higher mean, which is the more accurate measure here. The mode does not represent the data sets well, and the median is too large of a spread too.
Question 3
a) $x=3$, $y=8$
b) $x=22$, $y=22$
c) $x=5$, $y=6$, $z=12$
d) $4,4$ and $6$
e) $23,23,25,33$
f) $23,24,46,46,46$
Question 1
Find the mode, range, mean and median for the following data sets:
a) $2,3,3,4,8$
b) $5,5,6,6,6,7,7$
c) $8,12,12,12,13,13,13,13$
d) $2,8,1,3,8,4,20,6$
e) $22,35,9,37,18,30,37,20$
f) $54,88,91,37,23,54,23,88,91,91$
g) $4.2,8.8,0.2,9.2$
h) $0.5,0.6,0.5,0.4,0.5,0.5$
i) $184,102,98,98,137,156,98,184$
j) $44.8,25.7,100,0.1,56.5,100,0.8,0.1,25.7,56.5,100$
Question 2
Compare the following data sets using the mode, range, mean and median:
a) Data set A: $4,5,7,9,10$
Data set B: $2,6,6,8,13$
b) Data set A: $18,16,43,18,13,12$
Data set B: $24,16,20,20,19,21$
c) Data set A: $19,4,1,25,1$
Data set B: $20,25,1,1,43$
Question 3
Answer the following worded questions
a) The range of the following data set is $11$ and the median is $8$. Find $x$ and $y$.
$x,5,y,8,14$
b) The median of the following data set is $22$ and the mean is $21$. Find $x$ and $y$.
$15,20,x,y,26$
c) The mode of the following data set is $5$, the range is 7 and the mean is $7$. Find $x$, $y$ and $z$.
$5,x,y,7,z$
d) Four numbers have a range of $6$, a mode of $4$ and a median of $5$. The largest number is $10$. Find the other three numbers.
e) Four numbers have a range of $10$ and mode of $23$ and a median of $24$. Find the four numbers.
f) Five numbers have a mode of $46$, a median of $46$, a range of $24$ and a mean of $37$. Find the five numbers.
Answers
Question 1
a) Mode is $3$
Range is $6$
Mean is $4$
Median is $3$
b) Mode is $6$
Range is $2$
Mean is $6$
Median is $6$
c) Mode is $13$
Range is $5$
Mean is $12$
Median is $12.5$
d) Mode is $8$
Range is $19$
Mean is $6.5$
Median is $5$
e) Mode is $37$
Range is $28$
Mean is $26$
Median is $26$
f) Mode is $91$
Range is $68$
Mean is $64$
Median is $71$
g) There is no Mode
Range is $8.6$
Mean is $5.6$
Median is $6.5$
h) Mode is $0.5$
Range is $0.2$
Mean is $0.5$
Median is $0.5$
i) Mode is both $98$ and $184$
Range is $86$
Mean is $137$
Median is $137$
j) Mode is $100$
Range is $99.9$
Mean is $46\frac{21}{55}$
Median is $44.8$
Question 2
a) Data set A:
No mode
Range is $6$
Mean is $7$
Median is $7$
Data set B:
Mode is $6$
Range is $11$
Mean is $7$
Median is $6$
Data set B is more varied according to the range, however their average ability is the same as they have the same range.
b) Data set A:
Mode is $18$
Range is $31$
Mean is $20$
Median is $17$
Data set B:
Mode is $20$
Range is $8$
Mean is $20$
Median is $20$
Data set A is more varied according to the range, however their average ability is the same as they have the same range. $43$ in Data Set A seems like an outlier, as is a much higher result. It may be necessary to retest this result. If it wasn't for $43$ Data Set B would have an overall higher average with a higher median.
c) Data set A:
Mode is $1$
Range is $24$
Mean is $10$
Median is $4$
Data set B:
Mode is $1$
Range is $20$
Mean is $45$
Median is $20$
. Data set B has a much higher mean, which is the more accurate measure here. The mode does not represent the data sets well, and the median is too large of a spread too.
Question 3
a) $x=3$, $y=8$
b) $x=22$, $y=22$
c) $x=5$, $y=6$, $z=12$
d) $4,4$ and $6$
e) $23,23,25,33$
f) $23,24,46,46,46$
Solutions
Question 1
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
Question 2
a)
b)
c)
Question 3
a)
b)
c)
d)
e)
f)