Question

Based on the frequency distribution given below ,compute the following statistical measures to characteristics the distribution
a. Co-efficient of variation
b. interquartile range
c. modal value

Annual Tax paid No. of messengers
(tk.thousand)
5-10 18
10-15 30
15-20 46
20-25 28
25-30 20
30-35 12
35-40 6​

Answer 1

Answer:

a. Co-efficient of variation = 105

b. interquartile range

         = Q3-Q1  = 11.12

c. modal value = 17.35

Step-by-step explanation:

tax paid    f        midvalue (x)    x²         fx          fx²

5-10          18         7.5               56.25    135        1012.5

10-15        30        12.5            156.25     375       4687.5

15-20       46        17.5           306.25     805       14087.5

20-25      28        22.5          506.25      630      14175.5

25-30       20      27.5            756.25     550        15125

30-35       12        32.5           1056.25     390       12675

35-40       6​          37.5           1406.25    225       8437.5

               158                                           3110        70200.5

mean = ∑fx÷n  = $\frac{3110}{158}$ = 19.6

standard deviation, SD = $\sqrt{\frac{summation \ fx^{2} }{n} - mean }$

                   = $\sqrt{ \frac{70200.5}{158} -19.6}$ = $\sqrt{424.7}$  = 20.6

a. Co-efficient of variation = $\frac{SD(100)}{mean}$ = $\frac{20.6(100)}{19.6}$  = 105.1

b. interquartile range

  Q1 = 13.58, Q3 = 24.71

interquartile range = Q3-Q1  = 24.71 - 13.38  = 11.12

c. modal value

maximum frequency is 46, corresponding class is 15-20

modal class 15-20

$mode = l+ \frac{h(f1-fo)}{2f1-f2-fo}$

l = 15, f1 = 46, fo = 30, f2 = 28, h= 5

$mode = 15+ \frac{5(46-30)}{92-30-28}$

modal value = 17.35