Math Problem Statement

The state test scores for

1212

randomly selected high school seniors are shown on the right. Complete parts​ (a) through​ (c) below.

Assume the population is normally distributed.

14221422

12251225

983983   692692

724724

834834

725725

750750

548548

620620

14411441

945945

Question content area bottom

Part 1

​(a) Find the sample mean.

x overbarxequals=909.1909.1

​(Round to one decimal place as​ needed.)

Part 2

​(b) Find the sample standard deviation.

sequals=enter your response here

​(Round to one decimal place as​ needed.)

Solution

To calculate the sample mean and sample standard deviation, let's follow the steps systematically.

Given Data:

The state test scores for 1212 randomly selected high school seniors are provided. However, the numbers are unclear or missing. From the provided scores:

  • 1422, 1422, 1225, 1225, 983, 983, 692, 692, 724, 724, 834, 834, 725, 725, 750, 750, 548, 548, 620, 620, 1441, 1441, 945, 945.

Part 1: Sample Mean (xˉ\bar{x})

The formula for the sample mean is:

xˉ=xin\bar{x} = \frac{\sum x_i}{n}

Where:

  • xix_i is each individual score,
  • nn is the total number of scores (1212).

Step 1: Sum the scores.

Let's calculate the total sum of these scores:

1422+1422+1225+1225+983+983+692+692+724+724+834+834+725+725+750+750+548+548+620+620+1441+1441+945+9451422 + 1422 + 1225 + 1225 + 983 + 983 + 692 + 692 + 724 + 724 + 834 + 834 + 725 + 725 + 750 + 750 + 548 + 548 + 620 + 620 + 1441 + 1441 + 945 + 945

Step 2: Find the sample mean.

Part 2: Sample Standard Deviation (ss)

The formula for the sample standard deviation is:

s=(xixˉ)2n1s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}

Where:

  • ( \sum (x_i -

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Measures of Central Tendency
Measures of Dispersion

Formulas

Sample Mean: x̄ = (Σx) / n
Sample Standard Deviation: s = sqrt(Σ(xi - x̄)^2 / (n - 1))

Theorems

Central Limit Theorem

Suitable Grade Level

Grades 10-12