Question

Corn plants from a test plot are measured, and the distribution of heights at 10-cm intervals is recorded in the following table:

Height (cm)	Plants (no.)
100	40
110	60
120	90
130	130
140	200
150	120
160	80
170	50
180	20

Calculate the mean height & Calculate the variance

Recall that the mean is calculated as ∑Xin where ∑Xi represents the sum of all individual values in the sample, and n is the number of individual values.

I really don't get this question so explanations with the correct formulas would be awesome thanks!!!

Answer 1

To get the mean height add all of the height measurements and divide them by nine because nine is the total number of numbers you added together. The result is the mean height.

100 +110 + 120 + 130 + 140 + 150 + 160 + 170 + 180 = 1260



140cm is the mean height.

To calculate the variance subtract the mean from each plant number.

40-140=-100
60-140=-80
90-140=-50
130-140=-10
200-140=60
120-140= -20
80-140=-60
50-140=-90
20-140= -120

Square each of the answers.
-100X-100=10000

-80X-80=6400

-50X-50=2500

-10X-10=100

60X60=3600

-20X-20=400

-60X-60=3600

-90X-90=8100

-120X-120=14400

Then add them together: 49,100 and divide by 9 to get the variance. The variance is 5,455.55 which averages up to 5456

The standard diviation is the squareroot of the variance, which is 73.86