Presentation is loading. Please wait.

Presentation is loading. Please wait.

Descriptive Statistics. Introduction  Data must be organized  Frequency distribution  Present data  Statistical graphs and charts.

Similar presentations


Presentation on theme: "Descriptive Statistics. Introduction  Data must be organized  Frequency distribution  Present data  Statistical graphs and charts."— Presentation transcript:

1 Descriptive Statistics

2 Introduction  Data must be organized  Frequency distribution  Present data  Statistical graphs and charts

3 Organizing Data  Frequency distribution  Uses classes and frequency  3 types  Categorical frequency distribution  Nominal - or ordinal- type data  Ungrouped frequency distribution  Grouped frequency distribution

4 Construct a Categorical Distribution  Make a table  ClassTallyFrequencyPercent  Tally the data  Count the tallies – frequency  Find the percentage  % = f/n * 100  f – frequency  n – total number

5 Example 2-1 ABBBAO OOB B BBOAO AOOO AOBA Twenty-five army inductees were given a blood test to determine their blood type. Construct a frequency distribution for the data.  Step 1: Make a table  Step 2: Tally the data  Step 3: Count the tallies  Step4: Find the percentage of values in each class

6 Example 2-1 Class A B O AB Frequency Percent 5/25 * 100 =20 7/25*100=28 9/25*100=36 4/25*100=16 Tally IIIII IIII II IIII

7 Ungrouped Frequency Distribution  Range of data is relatively small  Range = highest value – lowest value  Single data values for each class  Steps similar to categorical distribution  Make a table  Each unique data value is a class  Tally - Frequency  Percent or Relative Frequency  Rel. freq. = # of ea. value/ total # of values

8 Example A survey was taken on Maple Avenue. In each of 20 homes, people were asked how many cars were registered to their households. The results were recorded as follows: 1, 2, 1, 0, 3, 4, 0, 1, 1, 1, 2, 2, 3, 2, 3, 2, 1, 4, 0, 0 Construct a frequency distribution for the data.

9 Step 1: Make a table # of cars tally frequency rel. freq. Step 2: Tally – Frequency Step 3: Percent or Rel. Freq. # of CarsTallyFrequencyRel. Freq. 0IIII44/20 =.20 1IIII I66/20 =.30 2IIII55/20 =.25 3III33/20 =.15 4II22/20 =.10 Solution

10 Grouped Frequency Distribution  Range of data is large  Classes are more than 1 unit in width  Vocabulary  Class width – difference between consecutive lower class limits or upper class limits  31 – 24 = 7  37 – 30 = 7 Class Limits 24 – – – 44 Lower class limits Upper class limits

11 Grouped Frequency Distribution Class limitsClass boundaries 24 – – – – – – 44.5  Class boundaries  Always end in a 5  1 decimal place to right of data  If data are whole numbers  from lower limit  to upper limit  Class limits should have the same # of dec. places as the data

12 Guidelines for Classes  There should be between 5 and 20 classes  Class width should be an odd number  Midpoints will be integers instead of decimals  Classes must be mutually exclusive  No data value can fall into 2 classes  Classes must be continuous  No gaps  Even if there is no data in a class it must be included  Classes are exhaustive  All data fits into a class  Classes are equal in width  Only exception open-ended class

13 Constructing a grouped freq. distribution  Determine the number of classes  Find the highest and lowest values  Find the range  Select the # of classes (5 – 20)  Find the width  w = range/# of classes  Round up  3.2 becomes 4  3 becomes 4  Choose the lowest value as your starting point  Add the class width to this lower limit  Continue adding the width to the lower limits until you get the rest of the lower limits  Find the first upper limit  Subtract 1 from the second lower limit  Continue adding the width to find the remaining upper limits

14 Example done in parts These data represent the record high temperatures for each of the 50 states. Construct a grouped frequency distribution for the data using 7 classes

15 Class limits 100 – – – – – – Class limits Determine the # of classes Find the highest and lowest values H = 134 L = 100 Find the range: H – L ; R = 134 – 100 = 34 Select # of classes (already asks for 7) Find the class width: w = R/7; w = 34/7 = 4.9 ~ 5 Choose a starting point – lowest value = 100 Add the class width to find next lower limit Continue adding the width until there are 7 Find the first upper limit – subtract 1 from the second lower limit 105 – 1 = 104 Add the width to the upper limits + 5

16 Class boundaries & Class midpoints Class limits Class boundaries Class midpoints 100 – – – – – – – – – – – – – – Class midpoints determined by adding the 2 class limits together then dividing by 2 Or Adding the 2 class boundaries together then dividing by = 204/2 = 102

17 Constructing a grouped freq. distribution  Tally the data  Find the numerical frequencies from the tallies  Find the cumulative frequencies Class limits Class bound TallyFreq Cum. Freq 100 – – II – – IIII III – – IIII IIII IIII III – – IIII IIII III – – IIII II – – I – – I


Download ppt "Descriptive Statistics. Introduction  Data must be organized  Frequency distribution  Present data  Statistical graphs and charts."

Similar presentations


Ads by Google