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Published byLynn Bond Modified over 9 years ago
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Finding averages from the frequency table
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In this screencast Mean from frequency table Mean from frequency table with intervals Mode from frequency table Median from frequency table
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The Mean
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Find the total of the data and divide by the number of data items
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12, 12, 12, 15, 17, 17, 19, 19, 19
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Total is 142 Mean is 15.8
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12 x 3 + 15 x 1+17 x 2 + 19 x 3
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Mean from a frequency table
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Days absent (x) No of staff (f) 0126354 12141913974
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Days absent (x) No of staff (f) 0126354 12141913974 This is the variable
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Days absent (x) No of staff (f) 0126354 12141913974 This is the frequency This is the variable
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Days absent (x) No of staff (f) 0126354 12141913974 Sub-total X x F 0143839363524
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Days absent (x) No of staff (f) 0126354 12141913974 Sub-total X x F 0143839363524 78 186 T
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Days absent (x) No of staff (f) 0126354 12141913974 Sub-total X x F 0143839363524 78 186 T Mean = 186 / 78 = 2.38
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Intervals
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Height (mm) Frequency F 10 X 1515 X 20 712 20 X 25 15 25 X 30 3
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Height (mm) Frequency F 10 X 1515 X 20 712 Mid-point X 12.517.5 20 X 25 15 22.5 25 X 30 3 27.5
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Height (mm) Frequency F 10 X 1515 X 20 712 Mid-point X 12.517.5 Sub-total X x F 87.5210 20 X 25 15 22.5 337.5 25 X 30 3 27.5 82.5
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Height (mm) Frequency F 10 X 1515 X 20 712 Mid-point X 12.517.5 37 T Sub-total X x F 87.5210 20 X 25 15 22.5 337.5 25 X 30 3 27.5 82.5
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Height (mm) Frequency F 10 X 1515 X 20 712 Mid-point X 12.517.5 37 T Sub-total X x F 87.5210717.5 20 X 25 15 22.5 337.5 25 X 30 3 27.5 82.5
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Height (mm) Frequency F 10 X 1515 X 20 712 Mid-point X 12.517.5 37 T Sub-total X x F 87.5210717.5 20 X 25 15 22.5 337.5 25 X 30 3 27.5 82.5 Mean = 717.5 / 37 = 19.4 mm
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The mode
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The mode is the most common value in a data set
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Height (mm) Frequency F 10 X 1515 X 20 712 20 X 25 15 25 X 30 3
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Height (mm) Frequency F 10 X 1515 X 20 712 20 X 25 15 25 X 30 3 15 is largest frequency so 20 X 25 is the modal class
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Days absent (x) No of staff (f) 0126354 12141913974
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Days absent (x) No of staff (f) 0126354 12141913974 19 is largest frequency so 2 days is the most common absence period
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The median
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Median is value of ‘middle’ data item
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Height (mm) Frequency F 10 X 1515 X 20 712 20 X 25 15 25 X 30 3
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Height (mm) Frequency F 10 X 1515 X 20 712 20 X 25 15 25 X 30 3 Half of 37 is 18.5… 37 T
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Height (mm) Frequency F 10 X 1515 X 20 712 20 X 25 15 25 X 30 3 Cumulative frequency 719 3437
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Height (mm) Frequency F 10 X 1515 X 20 712 20 X 25 15 25 X 30 3 Cumulative frequency 719 3437 First value that is above 18.5
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Height (mm) Frequency F 10 X 1515 X 20 712 20 X 25 15 25 X 30 3 Cumulative frequency 719 3437 First value that is above 18.5 Median is in this interval
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Days absent (x) No of staff (f) 0126354 12141913974
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Days absent (x) No of staff (f) 0126354 1214191397478 T
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Days absent (x) No of staff (f) 0126354 1214191397478 T Half of 78 is 39…
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Days absent (x) No of staff (f) 0126354 1214191397478 T Cumulative Frequency 12264558677478
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Days absent (x) No of staff (f) 0126354 1214191397478 T Cumulative Frequency 12264558677478 First value that is above 39
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Days absent (x) No of staff (f) 0126354 1214191397478 T Cumulative Frequency 12264558677478 First value that is above 39 Median number of days absent is 2
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Summary
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Remember Mean: multiply midpoints by frequencies and add the sub-totals. Divide by the total of the frequencies Mode: find the largest frequency – the corresponding value is the modal value or modal class Median: calculate a running total of the frequencies – the first interval that is above half the total contains the median
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