Chapter 10, Problem 1CS

To determine

To find: the means and standard deviations for API and growth scores

Answer to Problem 1CS

In Alvord district:

Statistic	Mean	Standard deviation
API	756.42	40.08
Growth	271	17.95

In Riverside unified district:

Statistic	Mean	Standard deviation
API	806.85	43.12
Growth	14.78	12.67

Explanation of Solution

Given:

API and the growth scores for each of the two districts

Calculation:

Let’s find out means and standard deviations for API and growth scores for each of the two districts

API (1= Alvord schools and 2= riverside unified schools)

The mean is the sum of all values divided by the number of values:

  $\begin{array}{l}\overline{x_1}=\frac{786+760+768+745+731+815+690}{7}=756.4286\\ \overline{x_2}=\frac{\begin{array}{l}891+778+827+789+805+762+798+\\ 796+731+818+769+815+841+876\end{array}}{14}=806.8571\end{array}$

The sample standard deviation is the square root of the population sample

  $s_1=\sqrt{\frac{\begin{array}{l}{\left(786-756.4\right)}^2+{\left(760-756.4\right)}^2+{\left(768-756.4\right)}^2+\\ {\left(745-756.4\right)}^2+{\left(731-756.4\right)}^2+{\left(815-756.4\right)}^2+\\ {\left(690-756.4\right)}^2\end{array}}{7-1}}=40.08$

  $s_2=\sqrt{\frac{\begin{array}{l}{\left(891-806.85\right)}^2+{\left(778-806.85\right)}^2+{\left(827-806.85\right)}^2+{\left(789-806.85\right)}^2+\\ {\left(805-806.85\right)}^2+{\left(762-806.85\right)}^2+{\left(798-806.85\right)}^2+{\left(796-806.85\right)}^2+\\ {\left(731-806.85\right)}^2+{\left(818-806.85\right)}^2+{\left(769-806.85\right)}^2+{\left(815-806.85\right)}^2+\\ {\left(841-806.85\right)}^2+{\left(876-806.85\right)}^2\end{array}}{14-1}}=43.12$

Growth (1= Alvord schools and 2 = riverside unified schools)

  $\begin{array}{l}\overline{x_1}=\frac{-5-2+8+40-6+0-15}{7}=2.7143\\ \overline{x_2}=\frac{\begin{array}{l}18+8+10+23+28+6+35+\\ 34-4+28+3+7+8+3\end{array}}{14}=14.7857\end{array}$

The sample standard deviation is the square root of the population sample

  $\begin{array}{l}{s}_1=\sqrt{\frac{\begin{array}{l}{\left(-5-2.71\right)}^2+{\left(-2-2.71\right)}^2+{\left(8-2.71\right)}^2+\\ {\left(40-2.71\right)}^2+{\left(-6-2.71\right)}^2+{\left(0-2.71\right)}^2+\\ {\left(-16-2.71\right)}^2\end{array}}{7-1}}=17.9510\\ s_2=\sqrt{\frac{\begin{array}{l}{\left(18-14.78\right)}^2+{\left(8-14.78\right)}^2+{\left(10-14.78\right)}^2+{\left(23-14.78\right)}^2+\\ {\left(28-14.78\right)}^2+{\left(6-14.78\right)}^2+{\left(35-14.78\right)}^2+{\left(34-14.78\right)}^2+\\ {\left(-4-14.78\right)}^2+{\left(28-14.78\right)}^2+{\left(3-14.78\right)}^2+{\left(7-14.78\right)}^2+\\ {\left(8-14.78\right)}^2+{\left(3-14.78\right)}^2\end{array}}{14-1}}=12.6745\end{array}$

In Alvord district:

Statistic	Mean	Standard deviation
API	756.42	40.08
Growth	271	17.95

In Riverside unified district:

Statistic	Mean	Standard deviation
API	806.85	43.12
Growth	14.78	12.67

Conclusion:

Therefore, means and standard deviations for API and growth scoresare done