8. find the sample standard deviation of the following set of scores, correct to two decimal places, by…
8. find the sample standard deviation of the following set of scores, correct to two decimal places, by using the statistics mode on the calculator: 3, 20, 15, 10, 13, 20, 5, 20, 5, 20\nsample standard deviation = enter your next step here
Answer
Explicación:
Paso1: Calcular la media
La media $\bar{x}=\frac{3 + 20+15 + 10+13+20+5+20+5+20}{10}=\frac{141}{10}=14.1$
Paso2: Calcular las diferencias al cuadrado
$(3 - 14.1)^2=(- 11.1)^2 = 123.21$ $(20 - 14.1)^2=(5.9)^2=34.81$ $(15 - 14.1)^2=(0.9)^2 = 0.81$ $(10 - 14.1)^2=(-4.1)^2 = 16.81$ $(13 - 14.1)^2=(-1.1)^2 = 1.21$ $(20 - 14.1)^2=(5.9)^2=34.81$ $(5 - 14.1)^2=(-9.1)^2 = 82.81$ $(20 - 14.1)^2=(5.9)^2=34.81$ $(5 - 14.1)^2=(-9.1)^2 = 82.81$ $(20 - 14.1)^2=(5.9)^2=34.81$
Paso3: Sumar las diferencias al cuadrado
$S=123.21+34.81+0.81+16.81+1.21+34.81+82.81+34.81+82.81+34.81 = 466.7$
Paso4: Dividir por $n - 1$
$\frac{S}{n - 1}=\frac{466.7}{9}\approx51.86$
Paso5: Calcular la raíz cuadrada
La desviación estándar muestral $s=\sqrt{51.86}\approx7.20$
Respuesta:
$7.20$