# Statistics - Median

a - answer    s - solution    v - video    d - discussion

## 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 s v d
b) $5,7,9,11,13$a s v d
c) $25,26,30$a s v d
d) $44,52,68,77,78$a s v d
e) $4,4,5,7,8,9,9$a s v d
f) $23,23,25,25,27$a s v d
g) $44,79,104,130,877$a s v d
h) $2,2,2,3,3,3,4,4,4$a s v d
i) $8.2,19.3,25,27.8,30.2,36.7,48.9$a s v d
j) $0.4,0.5,0.5,0.7,0.8$a s v d
k) $0,0,6,8,20$a s v d
l) $-8,-2,-1$a s v d
m) $-50,-49,-3,-1,0$a s v d
n) $3,8,15,16,17,22,35,78,89,89,93$a s v d

## 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 s v d
b) $19,15,14,4,3$a s v d
c) $9,2,7$a s v d
d) $8,3,6,4,9$a s v d
e) $3,6,3,6,2,7,0,5,2$a s v d
f) $17,2,18$a s v d
g) $32,38,24,64,34$a s v d
h) $623,375,234,135,153,123,643$a s v d
i) $0.6,0.1,0.9,0.4,0.4$a s v d
j) $3.6,3.7,2.7,6.3,7.5,6.6,0.2,4.6,2.1$a s v d

## 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 s v d
b) $10,12$a s v d
c) $3,3$a s v d
d) $18,10$a s v d
e) $16,16,4,2$a s v d
f) $5,2,19,30$a s v d
g) $3,6,7,10$a s v d
h) $7,2,9,3$a s v d
i) $1,15,5,2,11,10,3,19$a s v d
j) $22,38,45,25,41,77$a s v d
k) $0.6,0.2,1.5,1.0$a s v d
l) $0.22,7.85,7.71,0.3,0.14,7.7,8.9$a s v d

## 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 16a s v d
b)
StemLeaf
58993
62466
70014

where 5|8 means 58 a s v d
c)
StemLeaf
1124469
1238
13122

where 11|2 means 112a s v d
d)
StemLeaf
25118
2636
2728
28011
298

where 25|1 means 251 a s v d

## 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 s v d

b) $135,139,140,142,146,152,152,168,177,188,189,189$a s v d

c) $27,34,18,22,8,4,33,22,31,15,18,20,28$a s v d

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 s v d

## Question 6

Find median from the following frequency table:

a)
ScoreFrequency
18
27
310
a s v d
b)
ScoreFrequency
114
1210
138
a s v d
c)
ScoreFrequency
887
898
9010
915
a s v d
d)
ScoreFrequency
128
134
1420
1525
164
173
a s v d
e)
MarkFrequency
014
118
222
335
424
527
610
a s v d

## Question 7

Find the answer to the following worded questions:

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

b) What is the median of the first $9$ odd numbers?a s v d

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 s v d

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 s v d