Grouped Frequency Calculating an estimate of the mean Jill Robertson.
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Transcript of Grouped Frequency Calculating an estimate of the mean Jill Robertson.
![Page 1: Grouped Frequency Calculating an estimate of the mean Jill Robertson.](https://reader036.fdocuments.us/reader036/viewer/2022082612/56649f425503460f94c62620/html5/thumbnails/1.jpg)
Grouped Frequency
Calculating an estimate of the mean
Jill Robertson
![Page 2: Grouped Frequency Calculating an estimate of the mean Jill Robertson.](https://reader036.fdocuments.us/reader036/viewer/2022082612/56649f425503460f94c62620/html5/thumbnails/2.jpg)
Which is the modal class?
Weight 61 – 65 66 – 70 71 – 75 76 –80 81 - 85
Freq. 9 20 29 15 7
71 - 75
Question 1
A gardener checks the weights (in grams) of a number of tomatoes for grading purposes. Here are her results
Calculate an estimate for the mean
Weight 61 – 65 66 – 70 71 – 75 76 –80 81 - 85
Freq. 9 20 29 15 7
First of all we need a representative value for each group
Weight 61 – 65 66 – 70 71 – 75 76 –80 81 - 85
Freq. 9 20 29 15 7
63 68 73 78 83Mid-point
![Page 3: Grouped Frequency Calculating an estimate of the mean Jill Robertson.](https://reader036.fdocuments.us/reader036/viewer/2022082612/56649f425503460f94c62620/html5/thumbnails/3.jpg)
=
m 63 68 73 78 83
Weight 61 – 65 66 – 70 71 – 75 76 –80 81 - 85
Freq. 9 20 29 15 7
m x f
f
mfMean =
80
5795= 72.4375 = 72.4 (3 sf)
Now we need to calculate a total of the weight of tomatoes in each group
63 x 9567 68 x 201360 73 x 29 78 x 15 83 x 72117 1170 581
80
5795
We need to work out the total of our estimate of the weightand the total frequency
![Page 4: Grouped Frequency Calculating an estimate of the mean Jill Robertson.](https://reader036.fdocuments.us/reader036/viewer/2022082612/56649f425503460f94c62620/html5/thumbnails/4.jpg)
Why is this an estimate of the mean?
Because the data has been grouped and so exact data has been lost
![Page 5: Grouped Frequency Calculating an estimate of the mean Jill Robertson.](https://reader036.fdocuments.us/reader036/viewer/2022082612/56649f425503460f94c62620/html5/thumbnails/5.jpg)
Calculate an estimate of the mean for this distribution
Weight (Kg)
0-10 10-20 20-30 30-40 40-50 50-60
Frequency 11 18 16 11 5 2
Wt (Kg)
0-10 10-20 20-30 30-40 40-50 50-60
F 11 18 16 11 5 2
5 15 25 35 45Mid-point 55
63
14455 x 11 15 x 18 25 x 16 35 x 11 45 x 5 55 x 255 270 400 385 225 110
f
mfMean =
63
1445= 22.9365.. = 22.9 (3 sf)
m x f