# Statistics - Median

**Question 1**

To calculate the median, make sure the numbers are in order and then find the middle value. Find the median for the following:

a) $1,2,3,4,5$

a
$3$

Question ID: 70030010010

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b) $5,7,9,11,13$

a
$9$

Question ID: 70030010020

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c) $25,26,30$

a
$26$

Question ID: 70030010030

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d) $44,52,68,77,78$

a
$68$

Question ID: 70030010040

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e) $4,4,5,7,8,9,9$

a
$7$

Question ID: 70030010050

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f) $23,23,25,25,27$

a
$25$

Question ID: 70030010060

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g) $44,79,104,130,877$

a
$104$

Question ID: 70030010070

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h) $2,2,2,3,3,3,4,4,4$

a
$3$

Question ID: 70030010080

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i) $8.2,19.3,25,27.8,30.2,36.7,48.9$

a
$27.8$

Question ID: 70030010090

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j) $0.4,0.5,0.5,0.7,0.8$

a
$0.5$

Question ID: 70030010100

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k) $0,0,6,8,20$

a
$6$

Question ID: 70030010110

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l) $-8,-2,-1$

a
$-2$

Question ID: 70030010120

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m) $-50,-49,-3,-1,0$

a
$-3$

Question ID: 70030010130

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n) $3,8,15,16,17,22,35,78,89,89,93$

a
$22$

Question ID: 70030010140

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**Question 2**

To calculate the median, list the numbers in order and then find the middle value. Find the median for the following:

a) $7,6,2$

a
$6$

Question ID: 70030020010

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b) $19,15,14,4,3$

a
$14$

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c) $9,2,7$

a
$7$

Question ID: 70030020030

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d) $8,3,6,4,9$

a
$6$

Question ID: 70030020040

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e) $3,6,3,6,2,7,0,5,2$

a
$3$

Question ID: 70030020050

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f) $17,2,18$

a
$17$

Question ID: 70030020060

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g) $32,38,24,64,34$

a
$34$

Question ID: 70030020070

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h) $623,375,234,135,153,123,643$

a
$234$

Question ID: 70030020080

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i) $0.6,0.1,0.9,0.4,0.4$

a
$0.4$

Question ID: 70030020090

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j) $3.6,3.7,2.7,6.3,7.5,6.6,0.2,4.6,2.1$

a
$3.7$

Question ID: 70030020100

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**Question 3**

To find the median of an even number of values, list them in order, find the middle two values and find their mean/average. Find the median for the following:

a) $4,6,8,9$

a
$7$

Question ID: 70030030010

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b) $10,12$

a
$11$

Question ID: 70030030020

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c) $3,3$

a
$3$

Question ID: 70030030030

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d) $18,10$

a
$14$

Question ID: 70030030040

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e) $16,16,4,2$

a
$10$

Question ID: 70030030050

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f) $5,2,19,30$

a
$12$

Question ID: 70030030060

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g) $3,6,7,10$

a
$6.5$

Question ID: 70030030070

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h) $7,2,9,3$

a
$5$

Question ID: 70030030080

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i) $1,15,5,2,11,10,3,19$

a
$7.5$

Question ID: 70030030090

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j) $22,38,45,25,41,77$

a
$39.5$

Question ID: 70030030100

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k) $0.6,0.2,1.5,1.0$

a
$0.8$

Question ID: 70030030110

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l) $0.22,7.85,7.71,0.3,0.14,7.7,8.9$

a
$4$

Question ID: 70030030120

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**Question 4**

Find the median from the following stem and leaf diagram:

a)

Stem |
Leaf |

1 |
6 |
6 |
7 |

2 |
0 |
1 |
5 |

3 |
2 |
8 |
6 |

where 1|6 means 16

a
$21$

Question ID: 70030040010

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b)

where 5|8 means 58

a
$65$

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c)

where 11|2 means 112

a
$121$

Question ID: 70030040030

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d)

Stem | Leaf |
---|

25 | 1 | 1 | 8 |

26 | 3 | 6 | |

27 | 2 | 8 | |

28 | 0 | 1 | 1 |

29 | 8 | | |

where 25|1 means 251

a
$272$

Question ID: 70030040040

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**Question 5**

Form a stem and leaf diagram for the following data and find the median:

a) $42,45,47,51,59,68,69,72,77$

a

where 4|2 means 42

**The median is 9**

Question ID: 70030050010

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b) $135,139,140,142,146,152,152,168,177,188,189,189$

a
Stem | Leaf |
---|

13 | 5 | 9 | |

14 | 0 | 2 | 6 |

15 | 2 | 2 | |

16 | 8 | | |

17 | 7 | | |

18 | 8 | 9 | 9 |

where 13|5 means 135

**The median is 152**

Question ID: 70030050020

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c) $27,34,18,22,8,4,33,22,31,15,18,20,28$

a
Stem | Leaf |
---|

0 | 4 | 8 | | | |

1 | 5 | 8 | 8 | | |

2 | 0 | 2 | 2 | 7 | 8 |

3 | 1 | 3 | 4 | | |

where 0|4 means 4

**The median is 22**

Question ID: 70030050030

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d) $1.9,4.6,0.2,3.0,2.1,2.4,2.6,4.0,2.0,0.6,0.8,3.1,3.1,3.2,2.5,3.1,1.9$

a
Stem | Leaf |
---|

0 | 2 | 6 | 6 | 8 | |

1 | 9 | 9 | | | |

2 | 0 | 1 | 4 | 5 | |

3 | 0 | 1 | 1 | 1 | 2 |

4 | 0 | 6 | 8 | | |

where 0|2 means 0.2

**The median is 2.45**

Question ID: 70030050040

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**Question 6**

Find median from the following frequency table:

a)

a
$2$

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b)

a
$12$

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c)

Score | Frequency |
---|

88 | 7 |

89 | 8 |

90 | 10 |

91 | 5 |

a
$89.5$

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d)

Score | Frequency |
---|

12 | 8 |

13 | 4 |

14 | 20 |

15 | 25 |

16 | 4 |

17 | 3 |

a
$14$

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e)

Mark | Frequency |
---|

0 | 14 |

1 | 18 |

2 | 22 |

3 | 35 |

4 | 24 |

5 | 27 |

6 | 10 |

a
$3$

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**Question 7**

Find the answer to the following worded questions:

a) What is the median of the numbers from $1$ to $10$? (inclusive)

a
$5,5$

Question ID: 70030070010

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b) What is the median of the first $9$ odd numbers?

a
$9$

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c) What number must be taken away from the following list in order for the median to decrease by $1$?

$7,9,10,14,19$

a
$19$

Question ID: 70030070030

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d) What number can be added to the following list in order for the median to increase by $1$?

$27,13,8,18,1,22,4,11,15,20$

a
Any number less than or equal to $15$ works

Question ID: 70030070040

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**Question 1**

To calculate the median, make sure the numbers are in order and then find the middle value. Find the median for the following:

a) $1,2,3,4,5$

b) $5,7,9,11,13$

c) $25,26,30$

d) $44,52,68,77,78$

e) $4,4,5,7,8,9,9$

f) $23,23,25,25,27$

g) $44,79,104,130,877$

h) $2,2,2,3,3,3,4,4,4$

i) $8.2,19.3,25,27.8,30.2,36.7,48.9$

j) $0.4,0.5,0.5,0.7,0.8$

k) $0,0,6,8,20$

l) $-8,-2,-1$

m) $-50,-49,-3,-1,0$

n) $3,8,15,16,17,22,35,78,89,89,93$

**Question 2**

To calculate the median, list the numbers in order and then find the middle value. Find the median for the following:

a) $7,6,2$

b) $19,15,14,4,3$

c) $9,2,7$

d) $8,3,6,4,9$

e) $3,6,3,6,2,7,0,5,2$

f) $17,2,18$

g) $32,38,24,64,34$

h) $623,375,234,135,153,123,643$

i) $0.6,0.1,0.9,0.4,0.4$

j) $3.6,3.7,2.7,6.3,7.5,6.6,0.2,4.6,2.1$

**Question 3**

To find the median of an even number of values, list them in order, find the middle two values and find their mean/average. Find the median for the following:

a) $4,6,8,9$

b) $10,12$

c) $3,3$

d) $18,10$

e) $16,16,4,2$

f) $5,2,19,30$

g) $3,6,7,10$

h) $7,2,9,3$

i) $1,15,5,2,11,10,3,19$

j) $22,38,45,25,41,77$

k) $0.6,0.2,1.5,1.0$

l) $0.22,7.85,7.71,0.3,0.14,7.7,8.9$

**Question 4**

Find the median from the following stem and leaf diagram:

a)

Stem |
Leaf |

1 |
6 |
6 |
7 |

2 |
0 |
1 |
5 |

3 |
2 |
8 |
6 |

where 1|6 means 16

d)

Stem | Leaf |
---|

25 | 1 | 1 | 8 |

26 | 3 | 6 | |

27 | 2 | 8 | |

28 | 0 | 1 | 1 |

29 | 8 | | |

where 25|1 means 251

**Question 5**

Form a stem and leaf diagram for the following data and find the median:

a) $42,45,47,51,59,68,69,72,77$

b) $135,139,140,142,146,152,152,168,177,188,189,189$

c) $27,34,18,22,8,4,33,22,31,15,18,20,28$

d) $1.9,4.6,0.2,3.0,2.1,2.4,2.6,4.0,2.0,0.6,0.8,3.1,3.1,3.2,2.5,3.1,1.9$

**Question 6**

Find median from the following frequency table:

c)

Score | Frequency |
---|

88 | 7 |

89 | 8 |

90 | 10 |

91 | 5 |

d)

Score | Frequency |
---|

12 | 8 |

13 | 4 |

14 | 20 |

15 | 25 |

16 | 4 |

17 | 3 |

e)

Mark | Frequency |
---|

0 | 14 |

1 | 18 |

2 | 22 |

3 | 35 |

4 | 24 |

5 | 27 |

6 | 10 |

**Question 7**

Find the answer to the following worded questions:

a) What is the median of the numbers from $1$ to $10$? (inclusive)

b) What is the median of the first $9$ odd numbers?

c) What number must be taken away from the following list in order for the median to decrease by $1$?

$7,9,10,14,19$

d) What number can be added to the following list in order for the median to increase by $1$?

$27,13,8,18,1,22,4,11,15,20$

__Answers__

**Question 1**

a) $3$

b) $9$

c) $26$

d) $68$

e) $7$

f) $25$

g) $104$

h) $3$

i) $27.8$

j) $0.5$

k) $6$

l) $-2$

m) $-3$

n) $22$

**Question 2**

a) $6$

b) $14$

c) $7$

d) $6$

e) $3$

f) $17$

g) $34$

h) $234$

i) $0.4$

j) $3.7$

**Question 3**

a) $7$

b) $11$

c) $3$

d) $14$

e) $10$

f) $12$

g) $6.5$

h) $5$

i) $7.5$

j) $39.5$

k) $0.8$

l) $4$

**Question 4**

a) $21$

b) $65$

c) $121$

d) $272$

**Question 5**

a)

where 4|2 means 42

**The median is 9**
b)

Stem | Leaf |
---|

13 | 5 | 9 | |

14 | 0 | 2 | 6 |

15 | 2 | 2 | |

16 | 8 | | |

17 | 7 | | |

18 | 8 | 9 | 9 |

where 13|5 means 135

**The median is 152**
c)

Stem | Leaf |
---|

0 | 4 | 8 | | | |

1 | 5 | 8 | 8 | | |

2 | 0 | 2 | 2 | 7 | 8 |

3 | 1 | 3 | 4 | | |

where 0|4 means 4

**The median is 22**d)

Stem | Leaf |
---|

0 | 2 | 6 | 6 | 8 | |

1 | 9 | 9 | | | |

2 | 0 | 1 | 4 | 5 | |

3 | 0 | 1 | 1 | 1 | 2 |

4 | 0 | 6 | 8 | | |

where 0|2 means 0.2

**The median is 2.45**
**Question 6**

a) $2$

b) $12$

c) $89.5$

d) $14$

e) $3$

**Question 7**

a) $5,5$

b) $9$

c) $19$

d) Any number less than or equal to $15$ works

**Question 1**

To calculate the median, make sure the numbers are in order and then find the middle value. Find the median for the following:

a) $1,2,3,4,5$

b) $5,7,9,11,13$

c) $25,26,30$

d) $44,52,68,77,78$

e) $4,4,5,7,8,9,9$

f) $23,23,25,25,27$

g) $44,79,104,130,877$

h) $2,2,2,3,3,3,4,4,4$

i) $8.2,19.3,25,27.8,30.2,36.7,48.9$

j) $0.4,0.5,0.5,0.7,0.8$

k) $0,0,6,8,20$

l) $-8,-2,-1$

m) $-50,-49,-3,-1,0$

n) $3,8,15,16,17,22,35,78,89,89,93$

**Question 2**

To calculate the median, list the numbers in order and then find the middle value. Find the median for the following:

a) $7,6,2$

b) $19,15,14,4,3$

c) $9,2,7$

d) $8,3,6,4,9$

e) $3,6,3,6,2,7,0,5,2$

f) $17,2,18$

g) $32,38,24,64,34$

h) $623,375,234,135,153,123,643$

i) $0.6,0.1,0.9,0.4,0.4$

j) $3.6,3.7,2.7,6.3,7.5,6.6,0.2,4.6,2.1$

**Question 3**

To find the median of an even number of values, list them in order, find the middle two values and find their mean/average. Find the median for the following:

a) $4,6,8,9$

b) $10,12$

c) $3,3$

d) $18,10$

e) $16,16,4,2$

f) $5,2,19,30$

g) $3,6,7,10$

h) $7,2,9,3$

i) $1,15,5,2,11,10,3,19$

j) $22,38,45,25,41,77$

k) $0.6,0.2,1.5,1.0$

l) $0.22,7.85,7.71,0.3,0.14,7.7,8.9$

**Question 4**

Find the median from the following stem and leaf diagram:

a)

Stem |
Leaf |

1 |
6 |
6 |
7 |

2 |
0 |
1 |
5 |

3 |
2 |
8 |
6 |

where 1|6 means 16

d)

Stem | Leaf |
---|

25 | 1 | 1 | 8 |

26 | 3 | 6 | |

27 | 2 | 8 | |

28 | 0 | 1 | 1 |

29 | 8 | | |

where 25|1 means 251

**Question 5**

Form a stem and leaf diagram for the following data and find the median:

a) $42,45,47,51,59,68,69,72,77$

b) $135,139,140,142,146,152,152,168,177,188,189,189$

c) $27,34,18,22,8,4,33,22,31,15,18,20,28$

d) $1.9,4.6,0.2,3.0,2.1,2.4,2.6,4.0,2.0,0.6,0.8,3.1,3.1,3.2,2.5,3.1,1.9$

**Question 6**

Find median from the following frequency table:

c)

Score | Frequency |
---|

88 | 7 |

89 | 8 |

90 | 10 |

91 | 5 |

d)

Score | Frequency |
---|

12 | 8 |

13 | 4 |

14 | 20 |

15 | 25 |

16 | 4 |

17 | 3 |

e)

Mark | Frequency |
---|

0 | 14 |

1 | 18 |

2 | 22 |

3 | 35 |

4 | 24 |

5 | 27 |

6 | 10 |

**Question 7**

Find the answer to the following worded questions:

a) What is the median of the numbers from $1$ to $10$? (inclusive)

b) What is the median of the first $9$ odd numbers?

c) What number must be taken away from the following list in order for the median to decrease by $1$?

$7,9,10,14,19$

d) What number can be added to the following list in order for the median to increase by $1$?

$27,13,8,18,1,22,4,11,15,20$

__Answers__

**Question 1**

a) $3$

b) $9$

c) $26$

d) $68$

e) $7$

f) $25$

g) $104$

h) $3$

i) $27.8$

j) $0.5$

k) $6$

l) $-2$

m) $-3$

n) $22$

**Question 2**

a) $6$

b) $14$

c) $7$

d) $6$

e) $3$

f) $17$

g) $34$

h) $234$

i) $0.4$

j) $3.7$

**Question 3**

a) $7$

b) $11$

c) $3$

d) $14$

e) $10$

f) $12$

g) $6.5$

h) $5$

i) $7.5$

j) $39.5$

k) $0.8$

l) $4$

**Question 4**

a) $21$

b) $65$

c) $121$

d) $272$

**Question 5**

a)

where 4|2 means 42

**The median is 9**
b)

Stem | Leaf |
---|

13 | 5 | 9 | |

14 | 0 | 2 | 6 |

15 | 2 | 2 | |

16 | 8 | | |

17 | 7 | | |

18 | 8 | 9 | 9 |

where 13|5 means 135

**The median is 152**
c)

Stem | Leaf |
---|

0 | 4 | 8 | | | |

1 | 5 | 8 | 8 | | |

2 | 0 | 2 | 2 | 7 | 8 |

3 | 1 | 3 | 4 | | |

where 0|4 means 4

**The median is 22**d)

Stem | Leaf |
---|

0 | 2 | 6 | 6 | 8 | |

1 | 9 | 9 | | | |

2 | 0 | 1 | 4 | 5 | |

3 | 0 | 1 | 1 | 1 | 2 |

4 | 0 | 6 | 8 | | |

where 0|2 means 0.2

**The median is 2.45**
**Question 6**

a) $2$

b) $12$

c) $89.5$

d) $14$

e) $3$

**Question 7**

a) $5,5$

b) $9$

c) $19$

d) Any number less than or equal to $15$ works

__Solutions__

**Question 1**

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

m)

n)

**Question 2**

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

**Question 3**

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

**Question 4**

a)

b)

c)

d)

**Question 5**

a)

b)

c)

d)

**Question 6**

a)

b)

c)

d)

e)

**Question 7**

a)

b)

c)

d)