# 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)