Question

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

Answer 1

Answer:

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

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

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

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

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.

$\boxed{ \sf{mean = \frac{Σx}{N} }}$

$\dashrightarrow{ \sf{mean = \frac{120}{12} }}$

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

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

$\boxed{ \sf{median = { \frac{n + 1}{2} }^{th \: item}}}$

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

$\dashrightarrow{ \sf{median = {( \frac{13}{2}) }^{th \: }item }}$

$\dashrightarrow{ \sf{median = {6.5}^{th \: }}}$ item

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

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

$\dashrightarrow{ \sf{median = \frac{10 + 11}{2} }}$

$\dashrightarrow{ \sf{median = \frac{21}{2} }}$

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

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