Chapter 2 & 3

A concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The following data represent the strength of nine randomly selected casts (in psi): 3970, 4100, 3100, 3200, 2930, 3840, 4100, 4050, 3380 (a) What is the mean? (b) What is the median? (c) What is the mode?

(a) 3630 (b) 3840 (c) 4100

The following data represent the number of people in a particular state aged 18 to 67 with a high school education. 18-27: 200 28-37: 206 38-47: 191 48-57: 155 58-67: 190 (a) What is the number of classes? (b) What are the class limits for the second class? (c) What is the class width?

(a) 5 (b) Lower: 28 / Upper: 37 (c) 10

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule to determine the following: (a) What percentage of people has an IQ score between 87 and 113? (b) What percentage of people has an IQ score less than 87 or greater than 113? (c) What percentage of people has an IQ score greater than 139?

(a) 68% (b) 32% (c) 0.15%

What are the three Measures of Central Tendency?

- Mean - Median - Mode

What should the relative frequencies add up to?

1

Determine the original set of data. 1 | 0 1 6 2 | 1 4 4 7 8 3 | 3 5 5 5 7 9 4| 0 1

10, 11, 16, 21, 24, 24, 27, 28, 33, 35, 35, 35, 37, 39, 40, 41.

The following data represents the flight time (in minutes) of a random sample of seven flights from one city to another city. 284, 270, 260, 266, 257, 263, 269 What is the RANGE of flight time?

27 minutes

The following data represents the flight time (in minutes) of a random sample of seven flights from one city to another city. 284, 270, 260, 266, 257, 263, 269 What is the SAMPLE STANDARD DEVIATION of flight time?

8.8 minutes

Early in a presidential primary, a survey was conducted in which a random sample of 40 voters was asked which candidate, A through E, they would likely support for the nomination for president. The letter N indicates that the voter had no opinion. The results are provided below in a frequency distribution : (Candidate - Frequency) A - 5 B - 3 C - 3 D - 19 E - 6 N - 4 What is the Relative Frequency for each candidate?

A - 0.125 B - 0.075 C - 0.075 D - 0.475 E - 0.15 N - 0.1

Standard Deviation

A statistic used as a measure of the dispersion or variation in a distribution. Equal to the square root of the variance.

Frequency Distribution

A table with numeric categories and a frequency column with frequencies for each category; a table that lists each category of data and the number of occurrences for each category of data.

Variance

Based on deviation (spread) about the mean. However, the average deviation will be zero, so variance uses the sum of the squared deviations.

Interquartile Range

Difference between the 3rd quartile and the 1st quartile. IQR = Q3 - Q1.

Quartile

Divides the data, arranged in ascending order, into 4 equal sections. 1st: Q1 = 25th percentile 2nd: Median = 50th percentile 3rd: Q3 = 75th percentile

Outliers

Extreme values in the data set - they cannot be discarded. Must determine why they exist and how they affect the outcome.

Mean

Found by summing up the values of the data set and dividing the sum by the number of observations (average).

Relative Frequency

Frequency / Sample Size

Empirical Rule

In a normal distribution (bell-shaped), the Empirical Rule can estimate the percentage of data that falls within k standard deviations of the mean. • About 68% of the data values will fall within 1 standard deviation of the mean. • About 95% of the data values will fall within 2 standard deviations of the mean. • About 99.7% of the data values will fall within 3 standard deviations of the mean.

Class Limit

Lower Class Limit: The smallest possible value within a class (interval) Upper Class Limit: The largest possible value within a class (interval)

Measures of Position

Measures of position tell us the position that a particular data value has to the rest of the data set measures of position answer questions like: a school only grants admission to the top 10% of applicants -how high a score would you need to enter

Midrange

The arithmetic mean of the largest and the smallest values in a sample or other group

Class Midpoint

The average of each class (interval). To find class midpoint, take the average of the 2 consecutive lower class limits.

Measures of Dispersion

The degree or amount of spread in the data set. The larger the amount of spread, the larger the measurement will be.

Range

The difference between the largest value and the smallest value in the data set.

Z-Score

The distance a data value is from the mean in terms of the number of standard deviations.

Percentile

The kth percentile, denoted Pk, of a set of data is a value such that k percent of the observations are less than or equal to the value.

Frequency

The number of observations in each category.

Median

The value that lies in the middle of the data once the data has been arranged in ascending order (from smallest to largest).

Mode

The value that occurs most often or has the highest frequency.

How many Modes can there be?

There can be no mode, one mode, two modes (bimodal), or several modes (multi-modal).

Measures of Central Tendency

XXX

The ______ is the only measure of central tendency that can be used on both quantitative and qualitative data.

mode

The _________ represents the number of standard deviations an observation is from the mean.

z-score