Question

Find each value of the five-number summary for this set of data. [Note: Type your answers as numbers. Do not round.] 46, 19, 38, 27, 12, 38, 51 minimum maximum median upper quartile lower quartile

Answer 1

Answer:

Maximum : 51

Minimum: 12

Median: 38

Lower quartile: 19

Upper quartile: 46

Step-by-step explanation:

To answer this question, we first order the data from largest to smallest:

46, 19, 38, 27, 12, 38, 51

12, 19, 27, 38, 38, 46, 51

It can be seen that the maximum value is:

51

The minimum value is

12

Let's call N the amount of data.

To calculate the quartiles we use the following formula:

$Q_1 = X_{\frac{1}{4}(N + 1)}$

So:

$Q_1 = X_{\frac{1}{4}(7 + 1)}$

$Q_1 = X_2$

Where $X_2$ is the data number 2.

Q1 = 19

As the number of data is imapar, then, the median is the central data:

12, 19, 27, {38}, 38, 46, 51

Median = 38

Finally:

$Q_3 = X_ {\frac{3}{4}(n + 1)}\\\\Q_3 = X_ {6}$

Where $X_6$ represents the data number 6

$Q_3 = 46$