IB Mathematics SL 4.12 Standardization of normal variables AA SL Paper 1- Exam Style Questions- New Syllabus

Question

Maya harvested 49 mangoes from her farm. The weights of the mangoes, \( w \), in grams, are shown in the following grouped frequency table.

Weight (g)	\( 100 \leq w < 200 \)	\( 200 \leq w < 300 \)	\( 300 \leq w < 400 \)	\( 400 \leq w < 500 \)	\( 500 \leq w < 600 \)
Frequency	4	7	14	16	8

Part (a):
Write down the modal group for these data. [1]

Part (b):
Use your graphic display calculator to find an estimate of the standard deviation of the weights of mangoes from this harvest. [2]

Part (c):
On the grid below, draw a histogram for the data in the table. [3]

▶️ Answer/Explanation

Solutions

Part (a)

Identify the modal group (highest frequency).

Frequencies: 4 (100–200), 7 (200–300), 14 (300–400), 16 (400–500), 8 (500–600).

Highest frequency is 16.

Answer: \( 400 \leq w < 500 \).

Part (b)

Estimate the standard deviation using midpoints and frequencies.

Midpoints: 150, 250, 350, 450, 550.

Using a graphic display calculator with grouped data: standard deviation \( \approx 115.265 \).

Answer: 115 g.

Part (c)

Draw a histogram with class widths of 100 g (100–200, 200–300, 300–400, 400–500, 500–600) and heights corresponding to frequencies 4, 7, 14, 16, 8.

Answer:

Histogram of Mango Weights

IB Mathematics SL 4.12 Standardization of normal variables AA SL Paper 1- Exam Style Questions