Finding Averages from Frequency Tables Here is the

Finding Averages from Frequency Tables Here is the data from a survey of girls shoe sizes 2 2 2 33334444455555556666677 To find the mode we look for the most common 6 To find the median we look for the middle number when put in order of size: 5 To find the mean we add them together and divide by how many there are: 4. 7 But we can make the calculation easier by putting it the data into a frequency table

Finding Averages from Frequency Tables 2 2 2 33334444455555556666677 How a frequency table is made Shoe Size (x) Data Frequency (f) fxx 3 4 5 7 9 2 6 12 20 35 54 14 2 3 4 5 6 7 or 2 x 3 Shoe size 2, 3 pieces of data, add them together 2+2+2 Shoe size 3, Shoe size 4, Shoe size 5, Shoe size 6, Shoe size 7 4 pieces of data, 5 pieces of data, 7 pieces of data, 9 pieces of data, 2 pieces of data 3 + 3 + 3 or 3 x 4 4 + 4 + 4 or 4 x 5 5 + 5 + 5 + 5 or 5 x 7 6 + 6 + 6 or 6 x 9 7+7 or 7 x 2 add them together add them together

Finding Averages from Frequency Tables Mean To calculate the mean we need to know what is the total and how many there are Shoe Size (x) Data 2 3 4 5 6 7 222 3333 44444 5555555 66666 7 7 Frequency (f) fxx 3 4 5 7 9 2 6 12 20 35 54 14 = 30 How many pieces of data are there altogether means the total or sum of What is the total of all the data added together? Add up the fx column = 141 So the mean is = 141 = 4. 7 30

Finding Averages from Frequency Tables Mode To find the mode we look for the most frequently appearing value – in other words the largest frequency Shoe Size (x) Data 2 3 4 5 6 7 222 3333 44444 5555555 66666 7 7 Frequency (f) fxx 3 4 5 7 9 2 6 12 20 35 54 14 because the shoe size 6 has the highest frequency (or there are more 6’s than any other number) shoe size 6 is the modal size mode = 6

Median Make a running total of the number at the end Finding Averages from Frequencyposition Tables of each data group. Shoe Size (x) Data 2 3 4 5 6 7 222 3333 44444 5555555 66666 7 7 fxx Frequency (f) 3 4 5 7 9 2 3 7 12 19 6 12 20 35 54 14 th and The median is the middle value when all the 15 data is placed in order The 16 th values of size (usually smallest to largest). Are in the Shoe size ‘ 5’ In a frequency table the values are already in order sizemedian Group so 5 isofthe There are 30 values in the table ( ) To find the position of the middle value we add 1 to the total frequency and half it 30 + 1 = 15. 5 The middle position is halfway between 2 15 and 16 Where is this in the table?

Finding Averages from Frequency Tables Now find the mean mode and median for this frequency table 1 3 7 12 2 6 16 15 15 54 Mode = 4 (highest frequency) Median position 12 + 1 = 6. 5 2 In the ‘ 4’ group Median = 4 54 12 = 4. 5