Measures of. U4 C 1.2 Dot plot and Histogram 2 January 15 16, 2015

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1 U4 C 1. Dot plot and Histogram January 15 16, 015 U 4 : C 1.1 CCSS. 9 1.S ID.1 Dot Plots and Histograms Objective: We will be able to represent data with plots on the real number line, using: Dot Plots Histograms and compare two sets of data on the same graph to make a decision. Dot Plot Includes all values from the range of the data and plots a point for each occurrence of an observed value on a number line. Histograms is a special type of bar graph. The horizontal axis represents a range of values, called an interval, instead single value or category. The vertical axis represents the frequency of data values in a equal interval. of a Which of the following two graph is a Dot Plot and Histogram? How do you know? Horizontal Axis Vertical Axis equal intervals of numerical data frequency Outlier A data point or an observation that is well outside of the expected range of values. Intervals space between two units,set of numbers consisting of all numbers between them. Maximum is the largest or the greatest value, quantity in a set of data. The period of highest, greatest, over a specific interval. (upper extreme) Minimum The smallest number in a finite set of numbers. A value of a function that is less than any other value of the function over a specific interval. (lower extreme) Frequency How often something happens (usually during a period of time). Ways to describe pattern of distribution are : Center (Location) Mean Median Mode Measures of Spread (variation) Variance Standard Deviation Shape Skewness pread data the degree to which data are spread out around Positively/Right their center. skewed Negative/Left Skewed

2 U4 C 1. Dot plot and Histogram January 15 16, 015 Center is located at the median of the distribution. This is the point in a graphic display where about half of the observations are on either side. In the chart to below the observations are centered over 4. Spread refers to the distribution of the data. If the observation cover a wide rage, the spread is large. If the observation are clustered around a single value, the spread is smaller. Mean The most common number in the distribution. To calculate it, add up the values of all terms and then divide by the number of terms. Median If the number of terms is odd, then the median is the number in the middle from an ordered set. If the number of terms is even, then the median is the average of the two numbers in the middle. Mode the greatest values subtracted from the least values in the distribution. Variation The extent to which data points are distribution or data set diverge from the mean value. Variability also refers to the extent to which these data points differ from each other (a lot, little or none). Standard Deviation Shape distribution is described by the following characteristics Symmetry, Skewness, Uniform. Symmetry. A symmetric distribution can be divided at the center so that each half is a mirror image of the other. Most measurements fall in the middle, and fewer fall at points farther away from the middle. Skewness. Tails: The thinner ends of a distribution are called tails. If one tail stretches out farther than the other the histogram is said to be skewed to the side of the longer tail. Tail Tail Uniform When the observations in a set of data are equally spread across the range of the distribution it is called a uniform distribution. A uniform distribution has no clear peaks. DOT PLOTS Step 1: Label your axis and title your graph. Draw a horizontal line and label it with the variable. Title your graph Step : Scale the axis based on the values of the variable Step 3: Mark a dot above the number on the horizontal axis corresponding to each data value. Dogs rescued by ASPCA Shelters Number of rescued dogs

3 U4 C 1. Dot plot and Histogram January 15 16, 015 Watch & Listen #1 Data was collected on the average resting heart rate of the students taking athletics Create a dot plot for the heart beat data: 1) Draw a number line that spans the data ) Place a dot for each of the data entries 3) Title the graph. Describe the overall pattern of the data we do The number of goals scored by each team in the first round of the California Southern Section Division V high school soccer playoffs is shown in the following table Create a dot plot for the above data and describe the overall pattern of data. 3 This table shows approximately how long it took members of Alicia's math class to complete a cross number puzzle. a) Show this data on a dot plot. b) What is the range of the data? 4 The students in one social studies class were asked how many brothers and sisters(siblings) they each have. The dot plot here shows the results. a) How many of the students have six siblings? b) How many of the students have no siblings? c) How many of the students have three or more siblings? Social Studies Class (Siblings) # of Siblings A histogram is like a bar graph but with no spaces between the bars. Histogram Step 1. Draw the axes. Label the vertical axis. Choose an appropriate scale and 0 mark equal intervals Step. Label horizontal axis and 14 list the age intervals Step 3. Draw a bar for each age 8 6 interval. Do not leave spaces 4 between the bars. 0 Step 4. Give the graph a title How to find # Interval? # of intervals = (how many #'s in the data set) How to find the Interval width? Interval width = # of intervals (Round the answer up) (Round the answer up)

4 U4 C 1. Dot plot and Histogram January 15 16, 015 # of intervals = (how many #'s in the data set) Interval width = # of intervals Many communities add fluoride to water to prevent tooth decay. In a 5 day period, these levels of fluoride were measured: 75, 86, 84, 85, 97, 94, 89, 84, 83, 89, 88, 78, 77, 76, 8, 7, 9, 105, 94, 83, 81, 85, 97, 93, 79 Find the interval width for the above data and frequency. Watch & Listen #5 Histograms: Describe the histogram's shape, spread, and center. How does the histogram compare to the dot plot drawn before? #of Heartbeats Count, frequency levels of fluoride Count, frequency we do 6 The Livingston High School Varsity Boy s basketball team had an excellent season, compiling a record of 15 5 (15 wins and 5 losses). The total points scored by the team for each o the 0 games are listed below in the order in which the games were played: 76, 55, 76, 64, 46, 91, 65, 46, 45, 53, 56, 53, 57, 67, 6, 64, 67, 5, 58, 6 (b) On the graph grid provided, create a (a) Complete the frequency table below. histogram using the frequency table from (a) above. 7 The following set of data represents the scores on a mathematics quiz: 58, 79, 81, 99, 68, 9, 76, 84, 53, 57, 81, 91, 77, 50, 65, 57, 51, 7, 84, 89 Complete the frequency table below and, on the accompanying grid, draw and label a frequency histogram of these scores. (a) In what interval does the median of this data set lie? (b) Describe the histogram.

5 Attachments U4C1.1 Dot Plots and Histograms wks.docx Unit 4 for Dot plot and Histogram.docx