Frequency distribution is missing, so i have attached it.
A)x¯ = 180.28
B)class 177 - 185
Step-by-step explanation:
A) For the class of 150 - 158;
the class boundaries will be 149.5 - 158.5.
Middle value(x_m) = (150 + 158)/2 = 154
Frequency(f) = 5.
f(x_m) = 154 × 5 = 770
For class of 159 - 167;
the class boundaries will be 158.5 - 167.5
Middle value (x_m) = (159 + 167)/2 = 163
Frequency(f) = 16
f(x_m) = 163 × 16 = 2608
For class of 168 - 176;
the class boundaries will be 167.5 - 176.5
Middle value (x_m) = (168 + 176)/2 = 172
Frequency(f) = 20
f(x_m) = 172 × 20 = 3440
For class of 177 - 185;
the class boundaries will be 176.5 - 185.5
Middle value (x_m) = (177 + 185)/2 = 181
Frequency(f) = 21
f(x_m) = 181 × 21 = 3801
For class of 186 - 194;
the class boundaries will be 185.5 - 194.5
Middle value (x_m) = (186 + 194)/2 = 190
Frequency(f) = 20
f(x_m) = 190 × 20 = 3800
For class of 195 - 203;
the class boundaries will be 194.5 - 203.5
Middle value (x_m) = (195 + 203)/2 =199
Frequency(f) = 15
f(x_m) = 199 × 15 = 2985
For class of 204 - 212;
the class boundaries will be 203.5 - 212.5
Middle value (x_m) = (204 + 212)/2=208
Frequency(f) = 3
f(x_m) = 208 × 3 = 624
Now,mean is;
x¯ = Σf(x_m)/Σf
Σf(x_m) = 770 + 2608 + 3440 + 3801 + 3800 + 2985 + 624 = 18028
Σf = 5 + 16 + 20 + 21 + 20 + 15 + 3 = 100
x¯ = 18028/100
x¯ = 180.28
B) Modal class is the class with the highest occurring frequency.
In this case, it's class 177 - 185 that has frequency of 21
