Write the empirical relation between mean, median and mode. (1) The mean of the following distribution is 18. Find the frequency f of the class 19 - 21.
Class 11-13 13-15 15-17 17-19 19-21 21-23
Frequency 3
6
9
13
f
5
23 - 25
4

class        midpoint (m)                     frequency(f)           fm

11-13                 12                                           3                    36

13-15                 14                                          6                    84

15-17                 16                                          9                   144

17-19                  18                                          13                 234

19-21                  20                                          f                   20f

21-23                  22                                          5                 110

23 - 25                 24                                          4                96

                                                                    ∑f= 40 +f       ∑fm= 704+20f

now

mean = ∑fm ÷ ∑f

18= 704 + 20f

         40+f

720 + 18f= 704 + 20f

16 = 2f

f = 8

For a moderately skewed distribution it is: If a frequency distribution has a symmetrical frequency curve, the mean, median and mode are equal

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.