Question

Find the measures of center for following. Data Frequency 30 - 34 1 35 - 39 0 40 - 44 3 45 - 49 7 50 - 54 5 55 - 59 10 60 - 64 10 65 - 69 21 70 - 74 12 mode

Answer 1

Answer: the mode is 67.2

Step-by-step explanation:

Given that;

Data               Frequency

30 - 34                 1

35 - 39                0

40 - 44                3

45 - 49                7

50 - 54                5

55 - 59               10

60 - 64               10

65 - 69              21

70 - 74               12

Mode = ?

we know that mode is the number that has the highest number of appearance of frequency, so in this case, the data group that has the highest frequency (21) is 65 - 69  

Lower class boundary of the modal group; L = 65

Frequency of the group before the modal group; Fm-1 = 10

Frequency of the modal group; Fm = 21

Frequency of the group after the modal group; Fm+1 = 12

Group width; G = 4

Now using the formula

Mode = L + [ (Fm - Fm-1) / ( (Fm - Fm-1) + (Fm - Fm+1) ) ] × W

so we substitute

Mode = 65 + [ (21 - 10) / ( (21 - 10) + (21 - 12) ) ] × 4

= 65 + [ 11 / 20] × 4

= 65 + 2.2

= 67.2    

Therefore the mode is 67.2