Purchase Solution

Frequency Distribution, Chebyshev's Theorem, and Statistics

Not what you're looking for?

Ask Custom Question

1. Given the following frequency distribution, find the mean, variance, and standard deviation.

2. Please show all of your work when answering the following:

Use Chebyshev's theorem to find what percent of the values will fall between 222 and 286 for a data set with a mean of 254 and standard deviation of 16.

Use the Empirical Rule to find what two values 95% of the data will fall between for a data set with a mean of 216 and standard deviation of 12.

Purchase this Solution

Solution Summary

Seven complete solutions for statistics problems related to descriptive statistics (mean, median, mode, range, variance, standard deviation, percentile and more). Includes a step by step solution for a problem related to Chebyshev's theorem.

Solution Preview

1. To determine the mean from the frequency table, you must first find the mid-point of each category. For example, the mid-point of the first category (61-63) is 62. You then multiply each mid-point by the frequency for that category. Sticking with the (61-63) category, you would multiply 62 by 19. Add all of the products together and divide by the sum of all frequency values.

Mean = 4, 221/63

= 67

To determine variance, we will use the following formula:

variance = sum of (x - mean)^2*f/n

where x is a mid-point value of a category, where f is the frequency of that category and n is the total frequency.

variance = [(62 - 67)^2*19] + [(65 - 67)^2]*17] + [(68 - 67)^2]*5] + [(71 - 67)^2]*10] + [(74 - 67)^2]*12]/63

= 1,296/63

= 20.57

Standard deviation is simply the square root of the variance, so ...

Purchase this Solution

Free BrainMass Quizzes
Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.