The following data gives the lengths, in cm, of 30... | WAEC SSCE - General Mathematics - 2002

Question 1 Report

The following data gives the lengths, in cm, of 30 pieces of iron rods :

45 55 65 60 61 68 59 54 64 76 50 68 72 68 80 67 70 62 79 67 64 63 71 59 64 53 57 74 55 57

(a) Using class intervals of 45 - 49, 50 - 54, 55 - 59, ... construct a frequency table of the data.

(b) Draw the histogram for the distribution

(d) What is the probability of selecting an iron rod whose length is in the modal class?

Answer

(a) Frequency table. Sorting the 30 lengths into the given class intervals and tallying gives:

Length (cm)	Tally	Frequency \(f\)	Midpoint \(x\)	\(fx\)
45 - 49	\|	1	47	47
50 - 54	\|\|\|	3	52	156
55 - 59	\|\|\|\| \|	6	57	342
60 - 64	\|\|\|\| \|\|	7	62	434
65 - 69	\|\|\|\| \|	6	67	402
70 - 74	\|\|\|\|	4	72	288
75 - 79	\|\|	2	77	154
80 - 84	\|	1	82	82
Total		30		1905

(b) Histogram of the distribution. The bars are drawn against the class boundaries \(44.5, 49.5, 54.5, 59.5, 64.5, 69.5, 74.5, 79.5, 84.5\) on the horizontal axis, with heights equal to the class frequencies. Since all class widths are equal, the bar heights are simply the frequencies.

graph — Histogram with bars spanning class boundaries 44.5-49.5, 49.5-54.5, ..., 79.5-84.5; the tallest bar is the modal class 60-64 with frequency 7.

(c) Mean of the distribution.

\[\bar{x}=\frac{\sum fx}{\sum f}=\frac{1905}{30}=63.5\text{ cm}.\]

(d) Probability of selecting a rod in the modal class. The modal class is the one with the highest frequency, \(60 - 64\) (frequency \(7\)). The number of rods in this class is \(7\) out of \(30\), so

\[P(\text{modal class})=\frac{7}{30}.\]

Read lesson note on Integration (JAMB)

Read lesson note on Probability (WAEC)

Read lesson note on Measures Of Location (JAMB)

Read lesson note on Statistics (WAEC)

Answer Details

(a) Frequency table. Sorting the 30 lengths into the given class intervals and tallying gives:

Length (cm)	Tally	Frequency \(f\)	Midpoint \(x\)	\(fx\)
45 - 49	\|	1	47	47
50 - 54	\|\|\|	3	52	156
55 - 59	\|\|\|\| \|	6	57	342
60 - 64	\|\|\|\| \|\|	7	62	434
65 - 69	\|\|\|\| \|	6	67	402
70 - 74	\|\|\|\|	4	72	288
75 - 79	\|\|	2	77	154
80 - 84	\|	1	82	82
Total		30		1905