Answer to Question #280411 in Statistics and Probability for chin

Question

A sample of college students was asked how much they spent daily on a cell phone plan (to the nearest peso).

Monthly Cell Phone Plan Cost (P)

Number of Students

10 - 18

6

19 - 27

8

28 - 36

10

37 - 45

7

what is the total frequency

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c} Classes & Lower & Upper & M_i & f_i & M_i\cdot f_i \\ \hline 10-18 & 10 & 18 & 14 & 6 & 84 \\ \hdashline 19-27 & 19 & 27 & 23 & 8 & 184 \\ \hdashline 28-36 & 28 & 36 & 32 & 10 & 320 \\ \hdashline 37-45 & 37 & 45 & 41 & 7 & 287 \\ \hdashline & & & Sum= & 31 & 875 \\ \hdashline \end{array}$$

Total frequency

$$\sum_if_i=6+8+10+7=31$$

$$mean=\bar{x}=\dfrac{1}{n}\sum_i(M_i\cdot f_i)$$

$$=\dfrac{1}{31}(14(6)+23(8)+31(10)+39(7))$$

$$=\dfrac{875}{31}\approx28.2258$$

Total frequency is $31.$

The sample mean for these grouped data is $\bar{x}=\dfrac{875}{31}\approx28.2258.$