Chapter 10, Problem 3MCQ

To determine

To calculate mean, median and mode on Sunnydale and Sun Valley

Answer to Problem 3MCQ

Sunnydale’s Mean is 90.14, median is 90, and mode is 90.

Sun Valley’s Mean is 91.14, median is 91, and mode is 91.

Explanation of Solution

Given information:

The temperature data set of Sunnydale and Sun Valley is,

Day	Sunnydale temperature	Sun Valley temperature
Sunday	95	80
Monday	88	86
Tuesday	86	91
Wednesday	90	102
Thursday	90	103
Friday	93	91
Saturday	89	85

Formula used:

Mean is,

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

Median is,

  $M={\frac{n+1}{2}}^{th}$

Mode is the maximum value or the most repeated value,

  $z=Most\mathrm{Re}peatedValue$

Calculation:

For Sunnydale,

For mean, substituting the values in the formula,

  $\overline{x}=\frac{95+88+86+90+90+93+89}{7}$

So,

  $\overline{x}=\frac{631}{7}$

On solving,

  $\overline{x}=90.14$

Hence, mean is 90.14

Re-arranging the data in ascending order,

86, 88, 89, 90, 90, 93, 95

For median, substituting the values in the formula,

  $M=\frac{7+1^{th}}{2}$

On solving,

  $M=4^{th}$

Substituting the values,

  $M=90$

Hence, median is 90

For mode, substituting the value,

  $z=90$

Hence, mode is 90

Therefore, Sunnydale’s Mean is 90.14, median is 90, and mode is 90.

For Sun Valley,

For mean, substituting the values in the formula,

  $\overline{x}=\frac{80+86+91+102+103+91+85}{7}$

So,

  $\overline{x}=\frac{638}{7}$

On solving,

  $\overline{x}=91.14$

Hence, mean is 91.14

Re-arranging the data in ascending order,

80, 85, 86, 91, 91, 102, 103

For median, substituting the values in the formula,

  $M=\frac{7+1^{th}}{2}$

On solving,

  $M=4^{th}$

Substituting the values,

  $M=91$

Hence, median is 91

For mode, substituting the value,

  $z=91$

Hence, mode is 91 Therefore, Sun Valley’s Mean is 91.14, median is 91, and mode is 91.