Chapter 10, Problem 11SGR

To determine

To calculate mean, median and mode.

Answer to Problem 11SGR

Mean is 85.5, median is 86.5, mode is 97

Explanation of Solution

Given information:

Aliyah’s first four science score are 91,72,97,82

Formula used:

Mean is,

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

Median is,

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

Mode is,

  $z=\max value$

Calculation:

Re-arranging the value in ascending values,

72,82,91,97

For mean, substituting the value,

  $\overline{x}=\frac{91+72+97+82}{4}$

So,

  $\overline{x}=\frac{342}{4}$

On solving,

  $\overline{x}=85.5$

Hence, mean is 85.5

For median, substituting the value,

  $M=\frac{{(\frac{4}{2})}^{th}+{(\frac{4}{2}+1)}^{th}}{2}$

On solving,

  $M=\frac{2^{nd}+3^{rd}}{2}$

Substituting the value,

  $M=\frac{82+91}{2}$

On solving,

  $M=86.5$

Hence, median is 86.5

For mode, substituting the value,

  $z=97$

Hence, mode is 97