Question

6. Use the data to find the following (Please show work)

2, 3, 5, 7, 8, 10, 11, 11, 13, 15, 17, 18
a. Mean
b. Median
C. Mode
d. Range

Answer 1

1.
`\boxed{ \boxed{ \sf{mean = 10}}}`

2.
`\boxed{ \boxed{ \sf{median = 10.5}}}`

3.
`\boxed{ \boxed{ \sf{mode = 11}}}`

4.
`\boxed{ \boxed{ \sf{range = 16}}}`

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.

`\boxed{ \sf{mean = (Σx)/(N) }}`

`\dashrightarrow{ \sf{mean = (120)/(12) }}`

`\dashrightarrow{ \sf{mean = 10}}`

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

`\boxed{ \sf{median = { (n + 1)/(2) }^(th \: item)}}`

`\dashrightarrow{ \sf{median = {( (12 + 1)/(2)) }^(th \: ) item}}`

`\dashrightarrow{ \sf{median = {( (13)/(2)) }^(th \: )item }}`

`\dashrightarrow{ \sf{median = {6.5}^(th \: )}}` item

`\sf{ {6.5}^(th) }` item is the average of 6 th and 7 th items.

`\sf{∴ \: median = \frac{ {6}^(th)item + {7}^(th) item}{2}}`

`\dashrightarrow{ \sf{median = (10 + 11)/(2) }}`

`\dashrightarrow{ \sf{median = (21)/(2) }}`

`\dashrightarrow{ \sf{median = 10.5}}`

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

`\boxed{ \sf{range = highest \: number - lowest \: number}}`

`\dashrightarrow{ \sf{range = 18 - 2}}`

`\dashrightarrow{ \sf{range = 16}}`

Hope I helped!

Best regards! :D