Consider the data : 12, 47, 8, 73, 18, 35, 39, 8, 29, 25, p. Which of the following number(s) could be p if the median of this data is 29? Class 8

Consider the data : 12, 47, 8, 73, 18, 35, 39, 8, 29, 25, p. Which of the following number(s) could be p if the median of this data is 29? Class 8

Question 1.

Consider the data : 12, 47, 8, 73, 18, 35, 39, 8, 29, 25, p. Which of the following number(s) could be p if the median of this data is 29? Class 8

(i) 10

(ii) 25

(iii) 40

(iv) 100

(v) 29

(vi) 47

(vii) 30

Solution:

(v) is the correct option for p.

Question 2.

The number of times students rode their cycles in a week is shown in the dot plot below. Four students rode their cycles twice in that week.

(i) Find the average number of times students rode their cycles.

(ii) Find the median number of times students rode their cycles.

(iii) Which of the following statements are valid? Why?

(a) Everyone used their cycle at least once.

(b) Almost everyone used their cycle a few times.

(c) There are some students who cycled more than once on some days.

(d) Exactly 5 students have used their cycles more than once on some days.

(e) The following week, if all of them cycled 1 more time than they did the previous week, what would be the average and median of the next week’s data?

Solution:

(i) Average

(ii) Median number of times =[latex]\frac{4+4}{2}[/latex] = 4.

(iii) (a) Not valid. 3 students did not use.

(b) Valid, as 39 out of 42 students used their cycles.

(c) Valid, which is very much clear from the given dot plot.

(d) Not valid, more than 5 students have used their cycles more than once on some days.

(e) Average be [latex]\frac{193}{42}[/latex] + 1 = [latex]\frac{193+42}{42}[/latex] = [latex]\frac{235}{42}[/latex]

and median will be [latex]\frac{4+4}{2}[/latex] = 4, because the median will be average of 21st and 22th observations.