Question

Elias measured the height, x, of each of the students in his class. He recorded the heights in the table below.

Calculate an estimate of the mean height of the students.
Give your answer in centimetres (cm).
Height (cm) 120 < * ≤ 130 130 < x s 140 140 < .* ≤ 150
Frequency
6
12
2

Please help, thanks!

Answer 1

To calculate the mean height of the students, we need to find the sum of all the heights and divide it by the total number of students.

First, we assign values to each height range. Let's assume the midpoint of each range represents the height for calculation:

Height Range Midpoint (x) Frequency

120 < x ≤ 130 125 6

130 < x ≤ 140 135 12

140 < x ≤ 150 145 2

To calculate the sum of the heights, we multiply each midpoint by its corresponding frequency and add them together:

Sum = (125 * 6) + (135 * 12) + (145 * 2)

Sum = 750 + 1620 + 290

Sum = 2660

Next, we calculate the total number of students by summing the frequencies:

Total students = 6 + 12 + 2

Total students = 20

Finally, we can calculate the mean height by dividing the sum of the heights by the total number of students:

Mean height = Sum / Total students

Mean height = 2660 / 20

Mean height = 133

Therefore, the estimated mean height of the students is 133 cm.