Chapter 10.3, Problem 1CYU

To determine

To calculate the five number summary.

Answer to Problem 1CYU

Five number summary is 99.99, 199.99, 299.99, 399.99, 439.99.

Explanation of Solution

Given information:

Price of smartphones at local store,

$199.99, $99.99, $249.99, $399.99, $439.99, $349.99

Formula used:

Five number summary is minimum, lower quartile, median, upper quartile, maximum.

Median is,

  $M=\frac{{(\frac{n}{2})}^{th}+{(\frac{n}{2}+1)}^{th}}{2}$ , where n is frequency

Lower quartile is,

  $Q1=(n+1)\times \frac{1}{4}$

Upper quartile is,

  $Q3=(n+1)\times \frac{3}{4}$

Minimum is the smallest value of the data set.

Maximum is the largest value of the data set.

Calculation:

Arranging the data in an ascending order,

$99.99, $199.99, $249.99, $349.99, $399.99, $439.99

For median,

Substituting the values in median formula,

  $M=\frac{{(\frac{6}{2})}^{th}+{(\frac{6}{2}+1)}^{th}}{2}term$

On solving,

  $M=\frac{3^{rd}+4^{th}}{2}term$

Substituting the value of 3^rd and 4^th observation,

  $M=\frac{249.99+349.99}{2}$

On solving,

  $M=299.99$

Hence, median is $299.99

For lower quartile,

Substituting the values in lower quartile formula,

  $Q1=(6+1)\times \frac{1}{4}$

So,

  $Q1=\frac{7}{4}$

On solving,

  $\begin{array}{l}Q1=1.7\\ \approx 2\end{array}$

Comparing the value with the dataset.

Hence, Lower quartile is 199.99.

For upper quartile,

Substituting the values in lower quartile formula,

  $Q3=(6+1)\times \frac{3}{4}$

So,

  $Q3=\frac{21}{4}$

On solving,

  $\begin{array}{l}Q3=5.2\\ \approx 5\end{array}$

Comparing the value with the dataset.

Hence, Upper quartile is 399.99

Minimum is the smallest value of the data set. Analyzing the data set 99.99 is the smallest value.

Hence, minimum is 99.99

Maximum is the largest value of the data set. Analyzing the data set 439.99 is the largest value.

Hence, maximum is 439.99.

Therefore, the five number summary is 99.99, 199.99, 299.99, 399.99, 439.99.