Elementary Statistics - Chapter 3

How to you calculate the percentile of a given P(sub number)?

Use the equation L = (k/100)*n K = the percentile being used, whatever the subnumber is on P n = the total number of values in the data set L = once solved will be used to locate the number in the data set, whatever L equals find that number on the list of the data set and that's your answer.

How do you find the z score?

Use the given value (x), subtract the mean, and divide the result by the standard deviation.

Which of the following is ALWAYS true: A. In a symmetric and​ bell-shaped distribution, the​ mean, median, and mode are the same. B. For skewed​ data, the mode is farther out in the longer tail than the median. C. Data skewed to the right have a longer left tail than right tail. D. The mean and median should be used to identify the shape of the distribution.

A. In a symmetric and​ bell-shaped distribution, the​ mean, median, and mode are the same.

Which of the following is NOT a value in the 5-number summary: A. Mean B. Qsub 1 C. Median D. Minimum

A. Mean

Which measure of variation is most sensitive to extreme scores? A. Range B. Mean C. Median D. Histogram

A. Range

Which of the following is NOT a property of standard deviation? A. When comparing variation in samples with very different​ means, it is good practice to compare the two sample standard deviations. B. The value of the standard deviation is never negative. C. The standard deviation is a measure of variation of all data values from the mean. D. The units of the standard deviation are the same as the units of the original data.

A. When comparing variation in samples with very different​ means, it is good practice to compare the two sample standard deviations.

Identify the symbols for the following: A. Sample Standard Deviation B. Population Standard Deviation C. Sample Variance D. Population Variance

A. s B. s² C. σ (called a "sigma") D. σ²

How do find the midrange of a data set?

Add the minimum value and the maximum value, then divide by 2.

Which of the following is NOT a measure of center? A. Mode B. Median C. Census D. Mean

C. Census

Which of the following is NOT a characteristic of the mean? A. The mean takes every data value into account. B. The mean is sensitive to outliers. C. The mean is relatively reliable. D. The mean is called the average by statisticians.

D. The mean is called the average by statisticians.

The value at the center or middle of a data set is a(n) _____________.

measure of center

What is the 5 number summary?

min, Q1, median, Q3, max (can calculate in statcrunch)

In modified boxplots, a data value is a(n) _________ if it is above Qsub 3 + (1.5)(IQR) or below Qsub 1 - (1.5)(IQR).

outlier

What is the range rule of thumb for estimating a value of the standard deviation?

range divided by 4

How do you find the mean of a frequency distribution?

Find the midpoint for each class (add the lowest number and the highest number of the class then divide by 2). Then multiply the midpoint by the number of frequencies for that class, then divide that result by the total number of frequencies for the sample. Do this for all classes and add up the means to get the total mean.

The measure of center that is the value that occurs with the greatest frequency is the ____________.

Mode

How do you fin the minimum and maximum numbers that are significantly high or low for z scores if you're only given the mean and the standard deviation?

Most z scores are low if they are less than or equal -2, and are high if they greater than or equal to 2. So set the z score equation equal to -2 to find the minimum and 2 to find the maximum, substituting in the mean and standard deviation. Your equation would be: (-2) or (2) = x - mean/std dev. Then solve for x.

How do you calculate the minimum and maximum possible numbers of a given data set that are within 1, 2, or 3 standard deviations of the mean?

Multiply the standard deviation by 1, 2, or 3, then subtract that amount from the mean to get the minimum, and add it to the mean to get the maximum.

What are quartiles?

Percentiles/quartiles are the main measures of non-parametric data spread. The 1st quartile has 25% of the data below it (Psub 25), the 2nd quartile corresponds to the median and has 50% of data below it (Psub 50), and the 3rd quartile has 75% of data below it (Psub 75).

How do you calculate the range?

Range = (maximum data value) - (minimum data value)

What is the range rule of thumb for identifying significant values?

Significantly Low = population mean - 2*(population standard deviation) Significantly high = population mean + 2(population standard deviation) Value Not Significant = between the above two formulas

Whenever a data value is less than the​ mean, _______.

the corresponding z-score is negative

What is a z score?

the number of standard deviations that a given value x is above or below the mean.

The square of the standard deviation is called the _______.

variance

How do you find a variance of a sample?

Take the Standard Deviation and square it. Make sure the answer is written in units squared.

How do you find the coefficient of variation?

Take the standard deviation, divide by the mean, then multiply the result by 100. (can use statcrunch)

What is a Emprical Rule?

The Empirical Rule states that for data sets having a distribution that is approximately bell shaped, the following applies: 1. about 68% of all values fall within 1 standard deviation of the mean. 2. about 95% of all values fall within 2 standard deviations of the mean. 3. about 99.7% of all values fall within 3 standard deviations of the mean.

What is the definition of percentile?

The measure of location, denoted by P(sub 1), P (sub 2) etc., which divide a set of data into 100 groups with about 1% of the values in each group.

How can you tell which boxplot is correct in a list of possible answers?

Wherever the box begins on the left is the beginning of Q1. If you know what Q1 is than you know where the box should begin.

Methods used that summarize or describe characteristics of data are called _________________ statistics.

descriptive

What is Chebyshev's Theorem?

at least (1 - 1/K²) of the items in any data set will be within K standard deviations of the mean, where K is any value greater than 1. Meaning: K=2: at least 3/4 (75%) of the data are within 2 standard deviations of the mean K=3: at least 8/9 (or 89%) of the data are within 3 standard deviations of the mean

The Range Rule of Thumb roughly estimates the standard deviation of a data set as _______.

s = range/4

A data value is considered​ _______ if its​ z-score is less than −2 or greater than 2.

significantly low or significantly high

How do you calculate percentile?

take the number of values that are less than the given value (x), divide by the total number of values from the data, and multiply the result by 100.

For data sets having a distribution that is approximately​ bell-shaped, _______ states that about​ 68% of all data values fall within one standard deviation from the mean.

the Empirical Rule

When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the​ mean, we call the new value a​ _______.

z-score