MATH 215 MIDTERM EXAM
QUESTIONS WITH VERIFIED
ANSWERS 2026
Statistics - ANSWERSscience of collecting, analyzing, presenting and interpreting data,
as well as making decisions based on such analyses
descriptive statistics - ANSWERSmethods for organizing, displaying and describing
data using tables, graphs and summary measures
data set - ANSWERSwhole set of numbers representing information
element - ANSWERSsubject or object about which information is collected
Inferential statistics - ANSWERSmethods that use sample results to help make
decisions or predictions about a population
Population - ANSWERSconsists of all elements whose characteristics are being studied
Sample - ANSWERSa portion of the population selected for study
Census - ANSWERSsurvey that includes every member of the population
Representative sample - ANSWERSsample that represents the characteristics of the
population as closely as possible
random sample - ANSWERSsample drawn in such a way that each element of the
population has a chance of being selected
variable - ANSWERScharacteristic under study that assumes different values for
different elements
observation - ANSWERSvalue of a variable for an element
Discrete variable - ANSWERSvariable hose values are countable, and can assume only
certain values with no intermediate values
continuous variable - ANSWERSvariable that can assume any numerical value over a
certain interval
cross-section data - ANSWERSdata collected on different elements at the same point in
time or for the same time period
, time series data - ANSWERSdata collected on the same element for the same variable
at different points in time
Raw data - ANSWERSdata recorded in the sequence in which they are collected,
before they are processed or ranked
Frequency distribution of a qualitative variable - ANSWERSlists all categories and the
number of elements that belong to that category
class boundary - ANSWERSgiven by the midpoint of the upper limit of one class and
the lower limit of the next class
class width - ANSWERSupper boundary - lower boundary
class midpoint - ANSWERSlower limit + upper limit / 2
class - ANSWERSan interval that includes all the values that fall within the lower and
upper limits, classes never overlap
Histograms - ANSWERSgraph used for frequencies, relative frequencies or
percentages (vertical axis) which are represented by the height of the bars, with the
bars adjacent to each other
classes on horizontal axis
Symmetric histogram - ANSWERSmean = median = mode
Histogram curve skewed right - ANSWERSlonger tail on the right
mean is the largest, mode is smallest and median is in the middle
Mode is always at the peak
Histogram curve skewed left - ANSWERSLonger tail on the left
mean is the smallest, mode is largest, median in the middle
Polygons - ANSWERSgraph formed by joining the midpoints of the tops of successive
bars in a histogram with straight lines, each end starts at zero
for very large data sets the curve eventually smooths
Ogives - ANSWERScurve drawn for cumulative frequency distribution by joining with
straight lines the dots marked above the upper boundaries of classes at heights equal to
the cumulative frequencies of respective classes
can be used to approximate cumulative frequency for any interval
Stem and leaf display - ANSWERSeach quantitative value is displayed with each value
divided into two portions
condenses information without losing information on individual observations
QUESTIONS WITH VERIFIED
ANSWERS 2026
Statistics - ANSWERSscience of collecting, analyzing, presenting and interpreting data,
as well as making decisions based on such analyses
descriptive statistics - ANSWERSmethods for organizing, displaying and describing
data using tables, graphs and summary measures
data set - ANSWERSwhole set of numbers representing information
element - ANSWERSsubject or object about which information is collected
Inferential statistics - ANSWERSmethods that use sample results to help make
decisions or predictions about a population
Population - ANSWERSconsists of all elements whose characteristics are being studied
Sample - ANSWERSa portion of the population selected for study
Census - ANSWERSsurvey that includes every member of the population
Representative sample - ANSWERSsample that represents the characteristics of the
population as closely as possible
random sample - ANSWERSsample drawn in such a way that each element of the
population has a chance of being selected
variable - ANSWERScharacteristic under study that assumes different values for
different elements
observation - ANSWERSvalue of a variable for an element
Discrete variable - ANSWERSvariable hose values are countable, and can assume only
certain values with no intermediate values
continuous variable - ANSWERSvariable that can assume any numerical value over a
certain interval
cross-section data - ANSWERSdata collected on different elements at the same point in
time or for the same time period
, time series data - ANSWERSdata collected on the same element for the same variable
at different points in time
Raw data - ANSWERSdata recorded in the sequence in which they are collected,
before they are processed or ranked
Frequency distribution of a qualitative variable - ANSWERSlists all categories and the
number of elements that belong to that category
class boundary - ANSWERSgiven by the midpoint of the upper limit of one class and
the lower limit of the next class
class width - ANSWERSupper boundary - lower boundary
class midpoint - ANSWERSlower limit + upper limit / 2
class - ANSWERSan interval that includes all the values that fall within the lower and
upper limits, classes never overlap
Histograms - ANSWERSgraph used for frequencies, relative frequencies or
percentages (vertical axis) which are represented by the height of the bars, with the
bars adjacent to each other
classes on horizontal axis
Symmetric histogram - ANSWERSmean = median = mode
Histogram curve skewed right - ANSWERSlonger tail on the right
mean is the largest, mode is smallest and median is in the middle
Mode is always at the peak
Histogram curve skewed left - ANSWERSLonger tail on the left
mean is the smallest, mode is largest, median in the middle
Polygons - ANSWERSgraph formed by joining the midpoints of the tops of successive
bars in a histogram with straight lines, each end starts at zero
for very large data sets the curve eventually smooths
Ogives - ANSWERScurve drawn for cumulative frequency distribution by joining with
straight lines the dots marked above the upper boundaries of classes at heights equal to
the cumulative frequencies of respective classes
can be used to approximate cumulative frequency for any interval
Stem and leaf display - ANSWERSeach quantitative value is displayed with each value
divided into two portions
condenses information without losing information on individual observations
