ISDS 161A Chapter 3 Terms

What does Chebyshev's theorem tell us?

It measures the percentage of observations falling between two equally distant standard deviations, from the mean, for a non-normal distribution.

A ____ distribution is characterized by one tail being longer than the other. a. normal b. skew

b. skew

____ can be measured by IQR, variance and standard deviation a. location b. spread

b. spread

A value has a z-score of 3. This means that a. That value is 3 standard deviations below the mean b. That value is 3 standard deviations above the mean c. That value is 3 standard deviations to the right of the median

b. the value is 3 standard deviations above the mean

Which of the following is not a measure of central location a. median b. variance c. mean d. mode

b. variance

Chebyshev's theorem only works when the standard deviation is greater than a. 0 b. 0.1 c. 1 d. 2

c. 1

A researcher has collected the following sample data. The mean of the sample is 5. 351232 The standard deviation is a. 16.5 b. 8.944 c. 4.062 d. 13.2

c. 4.062 (excel formula .stdev)

A histogram of a given data shows three clear peaks. This may mean that a. There are three distinct groups in the data b. There are three modes in the data c. Both a and b are correct

c. both a and b are correct

The median is a measure of a. relative dispersion b. relative location c. central location d. absolute dispersion

c. central location

The mean of a sample a. is computed by summing the data values and dividing the sum by (n-1) b. is always smaller than the mean of the population c. is computed by summing all the data values and dividing the sum by the number of items d. is always equal to the mean of the population

c. is computed by summing all the data values and dividing the sum by the number of items.

The histogram of a variable is symmetric, uni-modal and mound shaped. Then, a. mean > median b. mean < median c. mean = median

c. mean = median

The 50th percentile is the a. third quartile b. mean c. median d. mode

c. median

The variance of a sample of 169 observations equals 576. The standard deviation of the sample equals a. 28.561 b. 576 c. 13 d. 24

d. 24

Which of the following is a measure of variability a. percentiles b. quartiles c. geometric mean d. interquartile range (IQR)

d. IQR

The difference between the largest and the smallest data value is the a. IQR b. Coefficient of variation c. Variance d. Range

d. range

The mean moves away from the median in the direction of the

skew

What does the empirical rule measure?

the approximate percentage of observations falling between 1, 2 and 3 standard deviations from the mean for a normal distribution.

An outlier is a data point that is significantly different from what was expected. true false

true

Center, shape, and spread of a distribution describe what the graph of a distribution looks like true false

true

Descriptive statistics turns data into information using meaningful charts and numerical reports. true false

true

The IQR is the difference between Q3 and Q1. true false

true

The coefficient of variation measures the standard deviation relative to the mean. true false

true

The median is the point where 50% of the data lies above and 50% lies below. true false

true

The shape of a distribution can be characterized by symmetry, skewness, and modality true false

true

The standard deviation is the average spread from the mean. true false

true

What symbol represents the size of the population?

N

Students at a liberal arts college study for an average of 10 hours per week with a standard deviation of 2 hours per week. The distribution of their study time happens to be uni-modal, symmetric and bell shaped. Approximately 68% of students study between 8 and B hours a week. What is the value of B? a. 12 hrs b. 16 hrs c. 14 hrs d. none

a. 12 hours a day

Students at a liberal arts college study for an average of 10 hours per week with a standard deviation of 4 hours per week. The distribution of their study time happens to be skewed to left. At least 75% of students study between 2 and B hours a week. What is the value of B? a. 18 hrs b. 2 hrs c. 4 hrs d. none

a. 18 hours a day z-scores tell us how far x is from the mean. z = (2-10/4) = -2 so 2 is -2 s.d. away from the mean. this means B is +2 s.d. away from the mean. so s.d. = 4 hours per week, which means 2 s.d. = 8 8 to the right of the mean is 18. we can also plug 2 into z-score: 2=(B-10/4) 8=B-10 B=18

A researcher has collected the following sample data. The mean of the sample is 5 351232 a. 6 b. 2.25 c. 2 d. 9

a. 6

a histogram is symmetric. Then, a. it has no skewness b. it has only one mode c. its mean is greater than median

a. it has no skewness

____ can be characterized by the mean, median, and mode a. location b. shape

a. location

The measure of location which is the most likely to be influences by extreme values in the data set is the a. mean b. mode c. median d. range

a. mean

Which of the following provides a measure of central location for the data a. mean b. standard deviation c. range d. variance

a. mean

The variance can never be a. negative b. zero c. larger than the standard deviation d. smaller than the standard deviation

a. negative

The 75th percentile is referred to as the a. third quartile b. second quartile c. first quartile d. fourth quartile

a. third quartile

Which of the following symbols represents the mean of the population? a. μ b. σ2 c. N d. σ

a. μ

Which of the standard symbols represents the standard deviation of the population a. σ b. σ2 c. N d. μ

a. σ

From a random sample of 500 students, students study for an average of 10 hours per week with a standard deviation of 4 hours per week. Say, a student in this sample studies for 12 hours per week. What is the z-score of this student? a. 2 b. 0.5 c. 8

b. 0.5

The histogram of a quantitative variable is positively skewed. The mean of the variable is 35. Which one of the following is a more likely value of the median? a. 55 b. 30 c. 35

b. 30

A variable has Q1 of 25 and Q3 of 75. It also has a Q2 of 50. The IQR is. a. 25 b. 50 c. -50

b. 50

The IQR is the distance over which approximately ____ of the observations will fall. a. 25% b. 50% c. 75%

b. 50%

In a statistics mid-term exam graded out of 100 points, the distribution of the exam scores was a bi-modal with a mean of 70 points with a standard deviation of 10 points. What percentage of students scored between 40 points and 100 points? a. at least 70% b. at least 89% c. approximately 100%

b. 89% First, we must find the score. x-mean / s.d. 100-70 / 10 = 3 then use cheby: (1-1/z^2) x 100% 1-1/3^2 x 100% = 89%

The expected lower limit for data for a box plot has the formula a. Q1 + 1.5*IQR b. Q1 - 1.5*IQR

b. Q1 - 1.5*IQR

The expected upper limit for data for a box plot has the formula a. Q3 - 1.5*IQR b. Q3 + 1.5*IQR

b. Q3 + 1.5*IQR

Any value that lies above 3 standard deviations from the mean or below 3 standard deviations from the mean, for a normal distribution, will be considered a. a skew b. an outlier

b. an outlier

When data are positively skewed, the mean will usually be a. equal to the median b. greater than the median c. smaller than the median d. positive

b. greater than the median

a histogram is bi-modal. Then, a. it has one mode b. it has two modes c. it has three modes

b. it has two modes

The z-score measures the number of standard deviations from the a. mode b. mean

b. mean

Q2 is also known as a. mean b. median c. mode

b. median

If two groups of numbers have the same mean, then a. their modes must also be equal b. other measures of location need not be the same c. their medians must also be equal d. their standard deviations must also be equal

b. other measures of location need not be the same

When using a box-plot, a value outside of the whisker is considered a. median b. outlier c. standard deviation

b. outlier

μ is an example of a​ a. sample statistic. b. population parameter c. population variance d. mode

b. population paramter