Chapter 11, Problem 7CA

a.

To determine

To calculate x.

Answer to Problem 7CA

  $x=38$

Explanation of Solution

Given information:

Video game scores are,

36, 48, 42, 63, 28, x, 57, 52

Mean is 45.5

Formula used:

Mean is,

  $\overline{X}=\frac{{\displaystyle \sum x}}{n}$

Calculation:

For mean, substituting the values,

  $45.5=\frac{36+48+42+63+28+x+57+52}{8}$

So,

  $45.5=\frac{326+x}{8}$

Cross-multiplying,

  $364=326+x$

On solving,

  $x=38$

b.

To determine

To calculate x

Answer to Problem 7CA

  $x=46$

Explanation of Solution

Given information: Video game scores are,

36, 48, 42, 63, 28, x, 57, 52

Median is 47

Formula used:

Median is,

  $M=\frac{{(\frac{n}{2})}^{th}term+{(\frac{n}{2}+1)}^{th}term}{2}$

Calculation:

Re-arranging the data in ascending order,

28, 36, 42, 48, x, 52, 57, 63.

For median, substituting the values,

  $M=\frac{{(\frac{8}{2})}^{th}term+{(\frac{8}{2}+1)}^{th}term}{2}$

On solving,

  $M=\frac{4^{th}term+5^{th}term}{2}$

Substituting the values,

  $47=\frac{48+x}{2}$

So,

  $94=48+x$

On solving,

  $x=46$

c.

To determine

To calculate x.

Answer to Problem 7CA

  $x=63$

Explanation of Solution

Given information:

Video game scores are,

36, 48, 42, 63, 28, x, 57, 52

Mode is 63

Formula used:

Mode is,

  $Mode=Most\mathrm{Re}curringFrequency$

Calculation:

Since mode is the most recurring frequency, that is, the particular frequenct occurs the most number of times in a dataset.

Since mode is 63. Hence,

  $x=63$

d.

To determine

To calculate x

Answer to Problem 7CA

  $x=99$

Explanation of Solution

Given information: Video game scores are,

36, 48, 42, 63, 28, x, 57, 52

Range is 71

Formula used:

Range is,

  $range=\max -\min$

Calculation:

Re-arranging the data in ascending order,

28, 36, 42, 48, 52, 57, 63, x

Minimum value is 28

Maximum value is x.

Hence, substituting the values,

  $71=x-28$

Shifting the values,

  $x=71-28$

On solving,

  $x=99$