The table shows the heights of 40 plants. (a) State the modal class. (b)(i) Calculate the mean height of the…

Question

The table shows the heights of 40 plants. (a) State the modal class. (b)(i) Calculate the mean height of the plants. (ii) Calculate the standard deviation of the distribution.

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Part 18(a): State the modal class. Step 1: Identify the frequency for each class interval. The frequencies are 4, 8, 10, 12, 4, 2. Step 2: Determine the class interval with the highest frequency. The highest frequency is 12, which corresponds to the class interval 30 − 40. The modal class is 30 − 40. Part 18(b)(i): Calculate the mean height of the plants. Step 1: Find the midpoint (x) for each class interval and calculate fx. Heights of plants — Frequency (f) — Midpoint (x) — fx0 - 10 — 4 — 5 — 20 10 − 20 — 8 — 15 — 120 20 − 30 — 10 — 25 — 250 30 − 40 — 12 — 35 — 420 40 − 50 — 4 — 45 — 180 50 − 60 — 2 — 55 — 110 Total — ∑ f = 40 — ∑ fx = 1100 Step 2: Use the formula for the mean of grouped data. x = (∑ fx)/(∑ f); x = 1100/40; x = 27.5 The mean height of the plants is 27.5 cm. Part 18(b)(ii): Calculate the standard deviation of the distribution. Step 1: Calculate x² and fx² for each class. Heights of plants — Frequency (f) — Midpoint (x) — fx — x² — fx² | 0 − 10 | 4 | 5 | 20 | 25 | 1

The table shows the heights of 40 plants. (a) State the modal class. (b)(i) Calculate the mean height of the plants. (ii) Calculate the standard deviation of the distribution.

Step-by-step solution

Identify the frequency for each class interval.

Determine the class interval with the highest frequency.

Find the midpoint ( $x$ ) for each class interval and calculate $fx$ .

Use the formula for the mean of grouped data.

Calculate $x^2$ and $fx^2$ for each class.

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More Mathematics Questions

The table shows the heights of 40 plants. (a) State the modal class. (b)(i) Calculate the mean height of the plants. (ii) Calculate the standard deviation of the distribution.

Step-by-step solution

Identify the frequency for each class interval.

Determine the class interval with the highest frequency.

Find the midpoint (xxx) for each class interval and calculate fxfxfx.

Use the formula for the mean of grouped data.

Calculate x2x^2x2 and fx2fx^2fx2 for each class.

Still stuck on this one?

More Mathematics Questions

Find the midpoint ( $x$ ) for each class interval and calculate $fx$ .

Calculate $x^2$ and $fx^2$ for each class.