Data Handling. 1) the number of students in a class (you can't have half a student).

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1 Frequency Distributions Data Handling Learning Intention: By J. Portelli the end of the lesson you will be able to interpret frequency tables for grouped / ungrouped discrete and continuous data Frequency describes the number of times or how often a category, score, or range of scores occurs Data can either be Discrete or Continuous data. Discrete Data can only take certain values. Example: 1) the number of students in a class (you can't have half a student). 2)pair dice Example: the results of rolling 2 dice can only have the values 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 Continuous Data can take any value (within a range) Examples: 1) A person's height: could be any value (within the range of human heights), not just certain fixed heights, 2) Time in a race: you could even measure it to fractions of a second, 3) A dog's weight, State whether the following quantities could be discrete or continuous data: Data a) The number of pupils in a class. b) The time it took you to get to school on Monday. c) The number of peas in a pod. d) The length of your classroom. Discrete/ Continuous 1

2 Frequency distribution a summary display for a distribution of data A simple frequency distribution table consists of two columns: Regular (ungrouped) Frequency Distribution When a frequency distribution table lists all of the individual categories it is called an ungrouped frequency distribution. Example: x = number of naps toddlers take per day 2

3 Example: Students were asked to pick a number from The numbers chosen are listed below. Complete a frequency table: Grouped Frequency Distribution Sometimes, especially with continuous data, a set of scores covers a wide range of values. Example Group these numbers and complete a frequency table: 9,16,13,7,8,4,18,10,17,18,9,12,5,9,9,16,1,8,17,1, 10, 5,9,11,15,6,14,9,1,12,5,16,4,16,8,15,14,17 3

4 Mode, Median, Range and Mean of a set of Ungrouped Date An average is a single value that is typical of a set of data. J. Portelli Learning Intention: By the end of the lesson you will be able to interpret the mean, mode, median and range 1. Mode The mode, or modal value, is the value in the data that occurs most frequently. There is no mode when each number is repeated only once. 1, 10, 13, 7, 1, 3, 10, 1, 13, 1 Step 1 Arrange the numbers in order of size. 1, 1, 1, 1, 3, 7, 10, 10, 13, 13 Step 2 Find the number that is repeated the most. The mode is 1. Find the mode of the following: i. Shoe sizes: 40, 41, 36, 39, 42, 45, 40, 40, 41, 36, 40, 46, 39, 40, 42. ii. Number of sweets in a packet: 10,11,12,10,10,12,13,11,12,10,12, Median The median is the value in the middle of the data when it is arranged in order. Example: Find the median of the following numbers: 4, 10, 1, 5, 8. Step 1 Arrange the number in order of size. 1, 4, 5, 8, 10 Step2 Find the middle number (Remove one number from each side) 1, 4, 5, 8, 10 The median is 5 4

5 Example: Find the median of the following set of numbers: 7, 9, 10, 11, 3, 5, 5, 8 Step 1 Arrange the numbers in order of size. 3, 5, 5, 7, 8, 9, 10, 11 Step 2 Find the middle number 3, 5, 5, 7, 8, 9, 10, 11 The median is half way between 7 and 8. The median is 7.5 Find the median of: i. Shoe sizes: 3,4,6,3,7,5,4,5,4 ii. 19, 21,20, 17, 22, 18, 28, Range The range is a measure of spread: it describes how the data is spread out. The range = the highest value the lowest value Example: Find the range of the following set of numbers: 1, 3, 1, 10, 13, 7 Step 1 Step 2 Find the range of: Arrange the set of numbers in order of size. Range = Highest value Lowest value The range is 12. 1, 1, 3, 7, 10, = 12 i. Length of TV programmes: 1hr, 55min, 20mins, 45mins, 15mins, 55mins, 20mins. ii. Weight of school bag: 1kg, 2kg, 1.5kg, 1.75 kg, 0.5kg, 1.2kg, 1.5kg. 5

6 4. Mean The mean of a set of data is the sum of all the values divided by the number of values. Example : The temperature ( C) for each day in a particular week of were the following: 18, 19, 21, 20, 17, 15, 15. Step 1 Add all the numbers = 125 Step 2 Divide by the total number of values = Answer: The mean is C NOTICE: The mean is not always one of the values. Example: When Cristiano Ronaldo was playing for Manchester United he scored the following goals per season: : 4 goals : 5 goals : 9 goals : 17 goals : 31 goals : 18 goals Find the mean number of goals scored per season. 6

7 drawing a bar chart In a survey, students were asked what kind of transport they used to come to school. The following data was collected: Draw a bar chart. Learning Intention: By the end of the lesson you will be able to Draw and interpret bar charts 7

8 The frequency table below shows the marks obtained by Form 1 students in a Mathematics examination. Use the grid below to draw and label a bar chart to illustrate the above data. 8

9 Pie Charts A pie chart represents data on a circle. Each sector represents a category or class. Learning Intention: By the end of the lesson you will be able to Draw and interpret pie charts Look at this record of traffic travelling down a particular road. To draw a pie chart, we need to represent each part of the data as a proportion of 360, because there are 360 degrees in a circle. For example, if 55 out of 270 vehicles are vans, we will represent this on the circle as a segment with an angle of: This will give the following results: This data is represented on the pie chart below: 9