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222333344444555555566666666677 Finding Averages from Frequency Tables Here is the data from a survey of girls shoe sizes To find the mode we look for the most common6 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

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222333344444555555566666666677 Finding Averages from Frequency Tables Shoe size 2, 3 pieces of data,add them together 2 + 2 + 2 or 2 x 3 Frequency (f) Shoe Size (x) Data 2 3 4 5 6 7 f x xf x x 36 Shoe size 3, 4 pieces of data, 4 add them together 3 + 3 + 3 + 3 or 4 x 5 12 Shoe size 4,5 pieces of data, 5 add them together4 + 4 + 4 + 4 + 4 or 3 x 4 20 How a frequency table is made or 5 x 7 Shoe size 5,7 pieces of data,add them together5 + 5 + 5 + 5 + 5 + 5 + 5 735 Shoe size 6,9 pieces of data,add them together 9 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 or 6 x 9 54 Shoe size 72 pieces of dataadd them together7 + 7 or 7 x 2 142

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Finding Averages from Frequency Tables Frequency (f) Shoe Size (x) Data 2 3 4 5 6 7 f x xf x x 36 412 520 Mean 735 954 142 222 3333 44444 555555 6 5 66666666 77 To calculate the mean we need to know what is the total and how many there are How many pieces of data are there altogether means the total or sum of = 30 What is the total of all the data added together? Add up the fx column = 141 So the mean is = 141 30 = 4.7

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Finding Averages from Frequency Tables Frequency (f) Shoe Size (x) Data 2 3 4 5 6 7 f x xf x x 36 412 520 Mode 735 954 142 222 3333 44444 555555 6 5 66666666 77 To find the mode we look for the most frequently appearing value – in other words the largest frequency because the shoe size 6 has the highest frequency (or there are more 6s than any other number) shoe size 6 is the modal size mode = 6

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Finding Averages from Frequency Tables Frequency (f) Shoe Size (x) Data 2 3 4 5 6 7 f x xf x x 36 412 520 Median 735 954 142 222 3333 44444 555555 6 5 66666666 77 The median is the middle value when all the data is placed in order of size (usually smallest to largest). In a frequency table the values are already in order of size 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 2 = 15.5 The middle position is halfway between 15 and 16 Where is this in the table? 3 7 12 19 Make a running total of the position number at the end of each data group. The 15 th and 16 th values Are in the Shoe size 5 Group so 5 is the median

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Finding Averages from Frequency Tables Now find the mean mode and median for this frequency table 2 6 16 15 12 54 12 = 4.5 Mode = 4 (highest frequency) 1 3 7 Median position 12 + 1 2 = 6.5 In the 4 group Median = 4

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