Question

Data on the number of calories (in '00) consumed daily by a sample of 15 year-old boys are given below.

Calories	1000-1500	1500-2000	2000-2500	2500-3000	3000-3500	3500-4000	4000-4500
No. of boys	5	13	16	18	27	10	4

Using the step-deviation method, find the mean calories consumed daily by a boy.

Answer 1

Take A = 2750, h = 500

Calories C.I.	Class Marks $\left(x_i\right)$	$$\begin{gathered} d_i=x_i-A \\ {d}_i=x_i-2750 \end{gathered}$$	$u_i=\frac{d_i}{h}=\frac{d_i}{500}$	No. of boys $\left(f_i\right)$	$f_i{u}_i$
1000-1500	1250	$-$1500	$-$3	5	$-$15
1500-2000	1750	$-$1000	$-$2	13	$-$26
2000-2500	2250	$-$500	$-$1	16	$-$16
2500-3000	$2750\to A$	0	0	18	0
3000-3500	3250	500	1	27	27
3500-4000	3750	1000	2	10	20
4000-4500	4250	1500	3	4	12
Total	-	-	-	$\sum _{}^{}{f}_i=93$	$\sum _{}^{}{f}_i{u}_i=2$

Now mean u_i s can be calculated as shown:

$$\begin{gathered} \overline{u}=\frac{{\displaystyle \sum _{}^{}}{f}_i{u}_i}{{\displaystyle \sum _{}^{}}{f}_i}=\frac{2}{93}=0.02 \\ \mathrm{Mean}=\overline{x}=A+h\overline{u} \\ =2750+500(0.02) \\ =2750-10 \\ =2740 \\ \therefore \mathrm{The}\mathrm{mean}\mathrm{calories}\mathrm{consumed}\mathrm{daily}\mathrm{by}\mathrm{a}\mathrm{boy}=2740. \end{gathered}$$