Answer:
1. [tex] \boxed{ \boxed{ \sf{mean = 10}}}[/tex]
2. [tex] \boxed{ \boxed{ \sf{median = 10.5}}}[/tex]
3. [tex] \boxed{ \boxed{ \sf{mode = 11}}}[/tex]
4. [tex] \boxed{ \boxed{ \sf{range = 16}}}[/tex]
Step-by-step explanation:
1. Given data : 2 , 3 , 5 , 7 , 8 , 10 , 11 , 11 , 13 , 15 , 17 , 18
Σx = 2 + 3 + 5 + 7 + 8 + 10 + 11 + 11 + 13 + 15 + 17 + 18 = 120
N ( total number of items ) = 12
Finding the mean
To find the mean, divide the sum of all the items by the number of items.
[tex] \boxed{ \sf{mean = \frac{Σx}{N} }}[/tex]
[tex] \dashrightarrow{ \sf{mean = \frac{120}{12} }}[/tex]
[tex] \dashrightarrow{ \sf{mean = 10}}[/tex]
Mean = 10
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2. Given data : 2 , 3 , 5 , 7 , 8 , 10 , 11 , 11 , 13 , 15 , 17 , 18
N ( total number of items ) = 12
Finding the position of median
[tex] \boxed{ \sf{median = { \frac{n + 1}{2} }^{th \: item}}} [/tex]
[tex] \dashrightarrow{ \sf{median = {( \frac{12 + 1}{2}) }^{th \: } item}}[/tex]
[tex] \dashrightarrow{ \sf{median = {( \frac{13}{2}) }^{th \: }item }}[/tex]
[tex] \dashrightarrow{ \sf{median = {6.5}^{th \: }}} [/tex] item
[tex] \sf{ {6.5}^{th} }[/tex] item is the average of 6 th and 7 th items.
[tex] \sf{∴ \: median = \frac{ {6}^{th}item + {7}^{th} item}{2}} [/tex]
[tex] \dashrightarrow{ \sf{median = \frac{10 + 11}{2} }}[/tex]
[tex] \dashrightarrow{ \sf{median = \frac{21}{2} }}[/tex]
[tex] \dashrightarrow{ \sf{median = 10.5}}[/tex]
Median = 10.5
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3. The mode of a set of data is the value with the highest frequency.
Given data : 2, 3, 5, 7, 8, 10, 11, 11, 13, 15, 17, 18
Here, 11 has the highest frequency.
So, Mode = 11
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4. Highest number = 18
Lowest number = 2
[tex] \boxed{ \sf{range = highest \: number - lowest \: number}}[/tex]
[tex] \dashrightarrow{ \sf{range = 18 - 2}}[/tex]
[tex] \dashrightarrow{ \sf{range = 16}}[/tex]
Hope I helped!
Best regards! :D
