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) Some students cycled more than once on some days.
(d) Exactly 5 students h

Question

Bright Tutorials · Accepted Answer

From the dot plot Data
(i) Sum = (0 × 3) + (1 × 1) + (2 × 4) + (3 × 7) + (4 × 7) + (5 × 5) + (6 × 4) + (7 × 6) + (8 × 3) + (10 × 2)
= 0 + 1 + 8 + 21 + 28 + 25 + 24 + 42 + 24 + 20
= 193
Total number of students = 42
Average = $\frac {193}{42}$ = 4.59 times
(ii) Total number of students = 42 (even)
So Median = average of 21st and 22nd terms
The 21st and 22nd terms lie in the cumulative frequency corresponding to 4.
So median = $\frac{4+4}{2}$ = 4
Median number of times students rode their cycles = 4
(iii) (a) Invalid
(b) Valid
(c) Valid
(d) Invalid
(e) Next week’s mean and median will be Mean = previous mean + 1
= 4.59 + 1
= 5.59
Median: Now the 21st and 22nd terms lie in the cumulative frequency corresponding to 5.
So Median = $\frac{5+5}{2}$ = 5

Tales by Dots and Lines — Question 10