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Mean = 74.57 Median = 72.5 Mode = 68.5

Step-by-step explanation:

Mean

In computing the mean for grouped data, use the formula

Mean = fM/n

f=class frequency

M=Midpoint or class mark

N=number of cases

Now let's solve first the midpoint.

Midpoint = (lower limit + upper limit)/2

Class Interval     Frequency      Midpoint        fM (Frequency x Midpoint)

89-99                         5                    94                                470

78-88                         6                     83                               498

67-77                         10                    72                               720

56-66                        9                    61                               549

30                                                       2237

Mean = fM/N

Mean = 2237/30

Mean = 74.57

Median

The formula in solving median of a grouped data is

Median = Xlb + i

X = lower boundary of median class

fm = frequency of the median class

i = class size

Class Interval     Frequency      Cumulative Frequency

89-99                         5                    30      (25+5)

78-88                         6                    25      (19+6)

67-77                         10                    19      (9+10)

56-66                        9                    9

30

To determine the median class, divide N by 2. Thus, 30/2 is equal to 15. Therefore, our median class is the classes with frequency of 10.

Class Interval     Frequency      Cumulative Frequency

89-99                         5                    30      (25+5)

78-88                         6                    25      (19+6)

67-77                         10                    19     (9+10)

56-66                        9                    9

30

Now let's solve for the median.

Median = Xlb + i

Median = 66.5 + 10

Median = 72.5

*lower boundary = lower limit - 0.5

*upper boundary = upper limit + 0.5

Mode

In solving the ode of a grouped data, we are going to use the formula

Mode = X + i

X = Lower boundary of the modal class

A = Difference of Highest frequency and the frequency below it

B =  Difference of Highest frequency and the frequency above it

To determine the modal class, look for the group with the highest frequency.

Class Interval     Frequency

89-99                         5

78-88                         6

67-77                         10

56-66                        9

30

Now let's solve for the mode.

Mode = X + i

Mode = 66.5 + 10