Study Hours Survey Analysis

00:00 8 marks

A survey was conducted on the number of hours students spend studying per week. The data collected from 150 students is summarized in the following table:

Hours (h)	Frequency
0 h < 5	15
5 1 h < 10	35
10 1 h < 15	55
15 1 h < 20	30
20 1 h < 25	10
25 01 h < 30	5

(a) Estimate the mean number of hours spent studying. [2]
(b) Estimate the standard deviation of the number of hours spent studying. [1]
(c) Find the median class. [1]
(d) Interpret the cumulative frequency curve provided for this data. [2]
(e) Based on the provided cumulative frequency curve, estimate the interquartile range. [2]

Part a

2 minutes 2 marks

Question

Estimate the mean number of hours spent studying. [2]

Hint Hint

Hint

Use mid-interval (class) values and frequencies in the mean formula.

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Complete Answer

Mean = 1875/150 = 12.50 hours

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Part b

1 minutes 1 marks

Question

Estimate the standard deviation of the number of hours spent studying. [1]

Hint Hint

Hint

Compute variance as a3f(xmean)b2/af, then take the square root.

Answer Answer
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Complete Answer

c3 5.68 hours

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Part c

1 minutes 1 marks

Question

Find the median class. [1]

Hint Hint

Hint

Determine the median position (N/2 = 75) using cumulative frequencies.

Answer Answer
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Complete Answer

10 01 h 3c 15

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Part d

2 minutes 2 marks

Question

Interpret the cumulative frequency curve provided for this data. [2]

Hint Hint

Hint

Examine the cumulative frequency at each upper class boundary and note the overall trend indicated by the curve.

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Complete Answer

The interpreted curve shows that the cumulative frequencies increase steadily through the points: (0,0), (5,15), (10,50), (15,105), (20,135), (25,145), (30,150).

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Part e

2 minutes 2 marks

Question

Based on the provided cumulative frequency curve, estimate the interquartile range. [2]

Hint Hint

Hint

Determine Q1 (at 150/4) and Q3 (at 3115O/4) from the curve, and then calculate the difference.

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Complete Answer

IQR 7.3 hours

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