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 ()
The formula for the sample mean is:
Where:
- is each individual score,
- is the total number of scores (1212).
Step 1: Sum the scores.
Let's calculate the total sum of these scores:
Step 2: Find the sample mean.
Part 2: Sample Standard Deviation ()
The formula for the sample standard deviation is:
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
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