Answer in Statistics and Probability for Shivam Nishad #88347

(i):

“L_x =(L_2+L_1)/2”“f_x=f cdot L_x”“Mean= frac {sum f_x} {sum f}=2850/50=57”

(ii):

“text {F – cumulative frequency}”“frac {sum f} {2} = 25 rightarrow text { class median: 56-58}”“L_m=55.5 text { – the lower boundary of the class median}”“f_m=21 text { – the frequency of the class median}”“F_m=15 text { – the cumulative frequency before class median}”“w=3 text { – the class width}”“Median=L_m + frac {frac {sum f} {2} – F_m} {f_m} w = 55.5 + frac {25-15} {21} 3 = 56.929”

(iii):

“f_{max} = 21 rightarrow text { modal group: 56-58}”“L_{md}=55.5 text { – the lower boundary of the modal group}”“f_{md} = 21 text { – the frequency of the modal group}”“Mode = L_{md} + frac {f_{md} – f_{md-1}} {(f_{md} – f_{md-1})+(f_{md} – f_{md+1})} w=”“=55.5+frac {21-10} {21-10+21-8} 3=56.875”

(iv):

“Variance=sigma ^2 = frac {sum f_x ^2} {sum f} – (frac {sum f_x } {sum f})^2 = frac {2162718} {50} – 57^2 = 40005.36”

(v):

“text {Standard deviation} = sqrt{sigma^2}=200.013”