The height of students at a school is shown as a cumulative frequency graph below. Use the graph to

Question

The height of students at a school is shown as a cumulative frequency graph below. Use the graph to estimate the median, the inter-quartile range. If $20$% of the students are taller than $h$ cm, find the value of $h$. Copy and complete the grouped frequency table of students' heights. Heights (cm)No. of students $120 \le x < 130$ $130 \le x < 140$ $140 \le x < 150$ $150 \le x < 160$ $160 \le x < 170$ $170 \le x < 180$ Using your grouped frequency table, calculate an estimate of the standard deviation. The students at the school took measurements of their weights using a faulty weighing machine. The box and whisker graph below shows the students' weights (in kg) measured by the faulty weight machine. If every student's true weight was actually $5$ kg lower, describe briefly how the box and whisker graph will differ from the given graph. State the correct value of the median weight.

Accepted Answer

(a)(i) $156\text{ cm}$ (a)(ii) $20\text{ cm}$ (b) $h=168\text{ cm}$ (c) Frequencies $60,100,260,310,280,190$ (d) $13.7\text{ cm}$ (3 s.f.) (e)(i) Translate the box-and-whisker plot $5\text{ kg}$ left, with unchanged spread (e)(ii) $57\text{ kg}$

Heights (cm)	No. of students
\(120 \le x < 130\)
\(130 \le x < 140\)
\(140 \le x < 150\)
\(150 \le x < 160\)
\(160 \le x < 170\)
\(170 \le x < 180\)

Statistics - Mean and Standard Deviation for Grouped Data

Statistics - Mean and Standard Deviation for Grouped Data

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