Bar Charts, Histograms, and Scatterplots

MTH 108          Bar Charts, Histograms, and Scatterplots ^1/27125

Two types of statistics

•  ____________________descriptive statistics          – techniques to describe or

 “summarize” data.

•  ______inferentia________l _statistics______: techniques to draw conclusions

or make inferences about a statistical “population” based on information obtained from a “sample”.

Frequency tables and visualizing  categorical data

•  _________________Frequency distribution________________________table          :

Shows how data are partitioned among several categories by listing the categories along with the number (frequency) of data values in each of them.

•  ____________________bar graph       (a.k.a. bar chart, bar plot) uses bars of equal width to show frequencies of categories of categorical (or nominal) data.

•  R Function for Barplots: barplot1)            barplot(sports -Expfrequencies)

•  Main argument for function:column ^of frequencies

Distributions of quantitative variables

•  ___distribution_________________: the nature or shape of the spread of the data over the range of values (such as bell shaped).

•  ___________________Frequency distribution _table_:show how data are partitioned among several categories (or classes) by listing the categories along with the number (frequency) of data values in each of them.

•  Relative frequency = class freq. / total freq. Percentage = Rel. frq. * 100

•  ____________________histogram         is a graph consisting of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values, and the vertical scale represents frequencies.

Important Uses of a Histogram:

        1.                                                                2.

        3.                                                         4.

Making a histogram.

The blood pressure of fourteen different second-year students in the university were measured. The systolic readings (mm Hg) are listed below: 5 classes

1381111111111 , 132 , 134 , 136 , 120 , 126 , 120 , 131 , 132 , 145 , 136 ,

138---, 129, 137

Visually display the shape of the distribution of the blood pressure data using histogram.

Step 1: Calculate the class width as shown below.

Step 2: Find minimum of data and add the class width to get the second lower class limit Step 3: Continue to add the class width until we have five lower class limits.

Step 4: Count how many data points fall into each interval (frequency table).

Step 5: On the vertical axis, place frequencies. On the horizontal axis, place the lower value of each interval.

            1) in+5= 105+5= 135

 ↑->+45 t

 213)                                                                                        - +5=

               1+5 ⁼ -

                                                                 125,

•  Function for scatter plots in R: hist()

•  Main argument for function: column of BP

Common distribution types

•  Normal distribution bellshaped-symmetrical

•  Uniform distribution flattop -every valvenas equal likelihood

•  Right-skewed distributionasymmetrical ^{-extreme high values}

•  Left-skewed distribution ^- asymmetrical ^{-extreme low values}

•  Bimodal distribution2peaks ^-_may indicate important division^{in a}

population

Paired quantitative variables

•  A _____________________scatterplot    is a graph of the relationship between two quantitative variables.

•  A scatterplot can be used as a visual aid in determining whether there is a correlation (or association) between the two variables.

Draw a scatter plot to illustrate the relationship between a bear’s chest size and weight.

Deceptive graphs

•  1. Non-zero vertical axis

•  2. Pictographs (the picture graph)